Cross-over of exponent values near the critical double point

Mixtures displaying gas-gas equilibria of the second kind are discussed on the basis of the geometry of the coexistence surface. If one approaches the critical double point isothermally the values of the critical exponents α, β, γ and ν are twice their “usual” values, whereas δ and η are “usual”. In a region above the critical-double-point temperature a cross-over effect occurs for isothermal approach of the critical line: close to critically the exponents are “usual” while further away from the critical state α, β, γ and ν are doubled. A simple expression for the cross-over pressure is derived. Consequences for the scaling relations are investigated.