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 \leftrightarrow hcp transformations in iron , which are sensitive to non-hydrostatic conditions and sample size .
From electronic-structure calculations , we find a bcc \leftrightarrow 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 .