National Physical Laboratory

Science of Eutectic Fixed-Points

Some of the science behind eutectic high-temperature fixed-points.

High Temperature Fixed Points

ITS-90 uses the freezing temperatures of pure metals as defined fixed-points up to 1084 °C (freezing temperature of copper). The benefits of higher-temperature fixed-points have long been realised, and the ITS-90 has recommended secondary reference values (Metrologia 33, pp 133-154 1996) based on freezing temperatures of elements up to ~3400 °C. However difficulties in using these higher-temperature fixed-points typically results in uncertainties of several degrees. Practical devices must be made out of materials that can withstand high temperatures, generally this involves using graphite. The ITS-90 defined fixed-points that have been used successfully are based on materials that do not alloy with carbon.

At higher temperatures, above the copper point, however things become more difficult. There are two important principles for high temperature work:

  • Everything reacts with everything else
  • It happens quickly

As a result many years of work and investigation failed to produce an acceptable and practical high temperature standard.

In 1999 Yoshiro Yamada of the AIST-NMIJ published a paper proposing the use of eutectic alloys of metal and carbon. NPL quickly realised the potential and has worked closely with NMIJ ever since, first to validate these fixed points for radiation thermometry and more recently, to use them for thermocouple calibrations.

Eutectic alloys

Pure metals that melt at higher temperature become polluted when heated in a graphite crucible. Melting and freezing takes place over a range and the mean melting and freezing temperature is changed.

The advantage of using eutectic alloys is that a unique temperature can be identified for a wide range of compositions. Regardless of the exact ratio of the two constituents some fraction will solidify at the eutectic composition. If one of the components is carbon then graphite crucibles and furnace tubes can be used without affecting the measured temperature even if small amounts of carbon/graphite continue to be dissolved into the fixed-point material.

Eutectic Phase Diagram
Figure 1: Phase diagram of an alloy with a eutectic reaction

Figure 1 shows what phases are present at a given composition and temperature for a mixture of two species of atom; A and B. In this case the possible phases are:

  • Liquid
  • Alpha, which comprises mostly species A with possibly a small amount of dissolved species B
  • Beta which is mostly species B with possibly a small amount of dissolved species A

In the phase diagram, a liquid starting at composition C(x) starts at point X and cools, following a path vertically down (i.e. the composition remains the same but the temperature is reduced). At T1 the liquidus (the highest temperature at which solid exists at a given composition and marked by the boundary of the liquid only region) is reached and solid starts to precipitate out of the liquid.

At any temperature between T1 and Te the system is a mixture of solid at a composition given by the orange line, and liquid at a composition given by the blue line. When Te is reached a eutectic reaction occurs:

  • At temperatures fractionally above Te the mixture of solid (either α or β but not both) and liquid has the lowest Gibbs free energy
  • At temperatures fractionally below Te the free energy is minimised with two solid phases
  • Therefore at Te there are three phases co-existing (solid α, solid β and α liquid)

The Gibbs phase rule says:

(degrees of freedom) = (number of constituents) - (number of phases) + 2

Here, we have two constituents and three phases so only one degree of freedom. That is we only need to specify one intensive quantity and we have fixed the system. If we make sure we fix the pressure then three phases can only be in equilibrium at a unique temperature; the eutectic temperature Te and a unique composition; the eutectic composition Ce.

Note that if the original alloy was hyper-eutectic rather than hypo-eutectic, say starting at the point Y, the situation is the same but β rather than α precipitates out above Te.

In the reverse case of melting, as the sample is heated liquid appears at Te at the interface between α and β phases and melting continues at this temperature until all the β phase is gone.

So eutectic alloys, while more complex to analyse than elemental fixed-points, offer the possibility of fixed-points that do not vary their melting or freezing temperature with use.

In Reality

It is important to realise that the previous analysis is based on the assumption of thermodynamic equilibrium. In principle it only applies when processes have an infinite time to equilibrate. We need to be aware of the possibility that a system is not in equilibrium when evaluating the behaviour of a fixed-point. Eutectic alloys will be more susceptible to non-equilibrium effects than elemental fixed-points because of the need to separate the uniform liquid into a differentiated arrangement of α and β solid:

Eutectic solidification

Eutectic Solidification
Figure 2: Eutectic solidification

Microstructure

A typical eutectic structure created during freezing is shown in figure 2. Note that the solid-liquid interface is curved and that the two solid phases are arranged in alternating layers. If the layers are more or less uniform the structure is said to be a 'regular' eutectic. If one phase has a marked tendency to grow in particular crystallographic directions, then converging and diverging layers are likely to give an 'irregular' eutectic.

Non-equilibrium considerations

The starting liquid is assumed uniform - the diffusion rates are ~1000 times faster in liquid than solid. In figure 3, if we follow the line from X to X’ we go from a uniform mixture of A and B atoms to the predominately A atom α-phase. A similar thing happens when following Y-Y’ to the β-phase. As A atoms are preferentially frozen into the α-phase B atoms are rejected. Therefore just in front of the α-phase the liquid is B rich. Conversely the liquid in front of the β-phase is A rich. These composition gradients result in sideways diffusion of the atoms. Since the composition is not at Ce freezing taking place at a temperature lower than Te - the liquidus lines now extend below Te.

Eutectic Non-Equilibrium
Figure 3: Non-equilibrium considerations

Therefore in a temperature gradient the solid-liquid interface will lag in some places and lead in others. It might at first seem that the interface temperature will vary. However there is another energy term involving the solid-liquid interface itself. The atoms at the boundary do not have the lowest energy bond arrangement. There is energy related to how curved the interface is; which depends on how the composition varies as this is what is causing the non-planar solidification front. If it is assumed that the thermal conductivity is high and the interface is at a fixed temperature then the varying composition and interface curvature can be analysed. This leads to the Jackson-Hunt model which links lamella spacing to the temperature of the eutectic freeze and agrees well with experiment. For this reason it is accepted that the interface is isothermal and that freezing takes place below the equilibrium eutectic temperature with an undercooling that depends on how fast solidification takes place. Fast freezing limits the diffusion, which causes bigger composition gradients, and so finer structure with more curvature at the interface, and so a larger undercool.

Eutectic SEM
Figure 4: Scanning electron microscope
image of cobalt-carbon eutectic. There
is an irregular arrangement of graphite
needles in a cobalt rich-phase matrix

Example of a metal-carbon eutectic alloy

With metal-carbon eutectics an irregular structure occurs. The covalent graphite bonds are directional so the freezing graphite phase grows along preferred directions relative to the original seed. In contrast, the metallic bonds of the metal rich phase have no preferred orientations. This faceting/non-faceting behaviour typically gives an irregular flake or needle morphology. It can also lead to non-coherence between the two phases - there is no way for the two lattices to match at phase interfaces. This can lead to high surface energy at phase boundaries. Since the amount of interface within a eutectic is also typically high this has lead to suggestions that interfacial energy is one reason why a eutectic alloy melts over a temperature range rather than a fixed temperature.

Last Updated: 14 Sep 2016
Created: 23 Oct 2007

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