Revision of Clausius–Clapeyron Relation for the First-Order Phase Transition in Ni–Mn–In Heusler Alloys

The derivation is presented of the Clausius-Clapeyron relation (CCR) in the second order of expansion of free energy potential on the change of temperature and magnetic field on the example of Ni-Mn-In Heusler alloys with the first-order metamagnetostructural phase transition (FOMMSPT), which can be treated as thermoelastic structural transition: austenite-martensite merging with metamagnetic transition: ferromagnet-antiferromagnet. It is shown that the second-order CCR describes satisfactory the nonlinear shift in the characteristic temperatures of the FOMMSPT in magnetic fields up to 25 T. It qualitatively and quantitatively explains the observed nonlinear dependence of the characteristic temperatures and the hysteresis of FOMMSPT including its elimination in some compositions of the Ni-Mn-In Heusler alloys under sufficiently high magnetic field.