Most of us are familiar with state diagrams that define which of the three states a substance will take given the pressure and temperature. And that some substances, such as water for example, exhibit the behavior of a triple point - a specific pressure and temperature at which the substance can exist in equilibrium between all three states. The Wikipedia image below illustrates the phase diagram and triple point.

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From the phase diagram one can also see that along any of the lines separating the liquid, solid and gas phases (green, red and blue lines) that the substance can exist in equilibrium between any two states.

Imagine though a substance that any one of the red, blue or green lines, is rather a long thin strip in which the third state exists. For example the green line in the diagram that separates liquid and solid would actually be a long barrow strip in which the gaseous state of the substance could exist. Thus you would have a triple point existing along a line at a set of pressures and temperatures.

Are there any substances (pure compounds or mixtures) that might at least approach this behavior?

Can theory predict the composition of substance by which a triple point line might occur. or do fundamental theories forbid it?

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    $\begingroup$ Gibbs phase rule is fairly straight forward, with the Wikipedia article easy to read. en.wikipedia.org/wiki/Phase_rule $\endgroup$ – Jon Custer May 25 '15 at 18:33
  • $\begingroup$ In principle this is not forbidden, but you would generically need three parameters to make probable the existence of tricritical lines. In addition to the pressure and temperature as in your example, the third dimension can be e.g. an electric or a magnetic field, ... then the area representing the phase in your diagram becomes volumes in a 3D space, and three 3D volumes can touch along a 1D-line without difficulty. I do not know any example of such system, but nothing forbids it for sure. PS: Your question is more about thermodynamics than any of the tag you used, so you should use it. $\endgroup$ – FraSchelle May 26 '15 at 22:13

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