A Matter of Size and Stress: Understanding the First‐Order Transition in Materials for Solid‐State Refrigeration

Abstract

Solid-state magnetic refrigeration is a high-potential, resource-efficient cooling technology. However, many challenges involving materials science and engineering need to be overcome to achieve an industry-ready technology. Caloric materials with a first-order transition-associated with a large volume expansion or contraction-appear to be the most promising because of their large adiabatic temperature and isothermal entropy changes. In this study, using experiment and simulation, it is demonstrated with the most promising magnetocaloric candidate materials, La-Fe-Si, Mn-Fe-P-Si, and Ni-Mn-In-Co, that the characteristics of the first-order transition are fundamentally determined by the evolution of mechanical stresses. This phenomenon is referred to as the stress-coupling mechanism. Furthermore, its applicability goes beyond magnetocaloric materials, since it describes the first-order transitions in multicaloric materials as well.under the application of an external field (i.e., electric, magnetic, mechanical stress, or pressure), as illustrated in Figure 1.Recently, the idea of utilizing not just one of these external fields, but a combination of multiple stimuli to transform the caloric material, was proposed, the so-called multicaloric effect. [15][16][17][18][19] In this study, we demonstrate that the caloric effect in materials with a first-order transition is always a consequence of multiple stimuli. Using the example of the three most promising magnetocaloric materials, La-Fe-Si, [20][21][22] Fe 2 P-type, [23][24][25][26] and Heusler alloys, [27][28][29] we develop a model from which the crucial role of mechanical stress is clear. This stress-coupling model does not involve any magnetism and is therefore immediately applicable to all the other caloric effects presented in Figure 1, helping us to understand first-order transitions in general. Cooling Technology

Coupling Phenomena in Magnetocaloric Materials

“…Materials such as La(Fe,Si) 13 , which undergo a considerable volume change (up to 1.5 vol %) during the transition, will choose a minimum energy path to transform, which has a direct impact on the nucleation sites of the transition. For a cubic or rectangular sample, regions close to the corners, which are the least constrained, can expand more easily than those in the center of the cube . Therefore, during the transition to the ferromagnetic state, which is connected with an increase in cell volume, the transition is likely to proceed from the corners across the entire surface and then towards the center.…”

“…This stress‐coupling mechanism has been suggested as an interpretation of experimental in situ X‐ray diffraction (XRD) data and from in situ magneto‐optical imaging . Recently, finite‐element simulations using a mechanically coupled ensemble of 1000 cubes confirmed this type of transition behavior . The observed existence of a long‐range elastic interaction between different parts of a sample led to the speculation that also in magnetocaloric Heusler compounds, the elastic stress originating from the volume change at the MT can influence nucleation patterns, and is even proposed to lead to “auto‐nucleation” of further nuclei in the strain field of a preceding nucleus .…”

“…It has been observed that the magnetocaloric effect depends to some degree on mechanical pulverization and hence particle size, and that the transformation can even be completely suppressed below a certain threshold size (e.g., in Mn–Fe–Ni–Ge) or enhanced by decreasing the particle size (for LaFe 11.8 Si 1.2 ). For magnetocaloric materials with magnetovolume (i.e., isostrucutral) transitions (e.g., LaFe 11.8 Si 1.2 and Mn 1.2 Fe 0.68 P 0.5 Si 0.66 ), a sharpening of the transformation, but at the same time a broadening of the thermal hysteresis, is observed upon reducing the particle size . Hence, the suppression of the transformation due to strain is preceded by an increase of hysteresis, progressively preventing the particle from transforming.…”

On the Optimization of Magneto‐Volume Coupling for Practical Applied Field Magnetic Refrigeration

“…A FOPT is associated with significant thermal and magnetic hysteresis that can drastically reduce the real cooling power . FOPT materials undergo a structural transition or a large volume change, simultaneously with the magnetic transition, which typically lead to crack formation and consequently to fast fatigue of the materials . Another drawback is the fact that, typically, FOPT materials do not transform completely under the low and practically achievable magnetic fields produced by permanent magnets, which hence hinders their full potential cooling power .…”

Reducing Hysteresis Losses by Heating Minor Loops in Magnetocaloric Ni–Mn–Ga–Co Films

“…All irreversible processes heat up the functional material and considerably reduce cooling efficiency. In Heusler alloys the martensitic transformation width tends to increase when sample size is reduced, which leads to significant broadening of the thermal hysteresis …”