  The coexistence pressure of two phases is a well-defined point at fixed
temperature. In experiment, however, due to non-hydrostatic stresses and a
stress-dependent potential energy barrier, different measurements yield
different ranges of pressure with a hysteresis. Accounting for these effects,
we propose an inequality for comparison of the theoretical value to a plurality
of measured intervals. We revisit decades of pressure experiments on the bcc -
hcp transformations in iron, which are sensitive to non-hydrostatic conditions
and sample size. From electronic-structure calculations, we find a bcc - hcp
coexistence pressure of 8.4 GPa. We construct the equation of state for
competing phases under hydrostatic pressure, compare to experiments and other
calculations, and address the observed pressure hysteresis and range of onset
pressures of the nucleating phase.
