Proving the contact rules for phase regions: Implications to phase diagrams of metal–hydrogen systems

• The paper considers binary metal–hydrogen systems with the hydrogen taken in excess.
• T–P diagrams of such systems are networks of triple points connected with lines.
• The rule of triple joints is valid for every triple point in these T–P diagrams.
• Boundary lines can be tangent to each other at the triple points.
• Sufficient conditions for applying the rule to T–x projections are formulated.

The rule of triple joints has recently been proved for two-dimensional phase diagrams and two-dimensional sections of phase diagrams of a higher dimension (Antonov, 2013). The present paper is extending this rule to phase diagrams of binary metal–hydrogen systems composed of a metal immersed in a hydrogen gas. The rule is shown to be valid for every triple point in the temperature–pressure phase diagrams of these systems, including the points with the intersecting boundary lines tangent to each other. The paper also considers the sufficient conditions for the application of the rule to triple points in the projections of phase diagrams onto the temperature–concentration plane.