We present some recent measurements of hysteresis, in materials undergoing big first order phase transformations, that resulted from a systematic program of tuning of the lattice parameters by changing composition. The lattice parameters were tuned so that a certain nongeneric condition of compatibility between phases was satisfied. An exceptionally sharp drop of size of the hysteresis of the transformation was observed at the special lattice parameters. The data has some fascinating features, including an apparent singularity. We re-examine the origins of hysteresis in light of these measurements, commenting in particular on a) the relation between static and thermodynamic approaches to hysteresis, b) the role of defects and pinning, c) the relation between hysteresis and fatigue life under repeated transformation, and d) the use of this kind of tuning to discover "unlikely" new materials. The relation between hysteresis and reversibility, together with the known extreme sensitivity of electromagnetic properties to lattice parameters, suggests that materials with unexpected properties may be discovered by this kind of tuning. Joint work with Jerry Zhang and Stefan Mueller.

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