Thermodynamics and Energy Conversion in Heusler Alloys

Abstract

Heusler alloys, particularly in the family Ni\(_2\)MnZ (Z \(=\) Ga, In, Sn and Sb) and nearby compositions, often exhibit martensitic phase transformation from a high-temperature cubic (L2\(_1\)) structure to a low-temperature, low-symmetry martensitic phase. These transformations are commonly accompanied by a change in magnetic ordering, due to the sensitivity of spin interactions to the change in interatomic distances and local symmetry. Various forms of energy can be made to interconvert during this multiferroic phase transformation. A particularly interesting family of alloys for this purpose is Ni\(_{50 - x}\)Co\(_x\)Mn\(_{25-y}\)Z\(_{y}\) (Z \(=\) Ga, In, Sn and Sb). Over a small compositional range, the phase transformation in these alloys is accompanied by a large change in magnetization—up to 1.2 MA/m (1200 emu/cm\(^3\)) in Ni\(_{45}\)Co\(_5\)Mn\(_{40}\)Sn\(_{10}\). In such materials it is possible to design an energy conversion device that directly converts heat to electricity using Faraday’s law of induction and cyclic phase transformation. Both the efficiency and work output per volume of such an energy conversion device are significantly affected by the size of the hysteresis , which is however tunable in these systems. A thermodynamic theory for such a energy conversion method is presented based on a free energy function that includes contributions from phase transformation and magnetism. Material constants in the free energy functions are determined by magnetic and calorimetric measurements. We give the estimates of efficiency and power output in terms of material constants, design parameters and working conditions for this energy conversion method. The first-order nature of the phase transformation, leading to an effect of magnetic field on transformation temperature and a mixed-phase region, play a critical role for the effectiveness of these methods.