Magnetostructural transformation and magnetocaloric effect of Sn-bonded Mn0.66Fe0.34Ni0.66Fe0.34Si0.66Ge0.34 composite

Magnetostructural coupling in MnMX (M = Co or Ni, X = Si or Ge) system attracts considerable attention for the accompanied multi-magnetoresponsive effects. However, due to the large stress generated from the structural transformation, the alloys become shattered or powder-like, hindering the further investigation and their applications. The possible solution is to embed the MnMX powders into metal matrix. In this paper, we choose Mn0.66Fe0.34Ni0.66Fe0.34Si0.66Ge0.34 as a representative of MnMX alloy and produce Mn0.66Fe0.34Ni0.66Fe0.34Si0.66Ge0.34/Sn composite bulk by hot pressing. The magnetostructural-coupled composites exhibit an improved rate of the transformation temperature shift by magnetic field and broadened operating temperature range. Additionally, we also propose a simple formula based on the entropy-temperature diagram to calculate the isothermal entropy change, which is consistent with the results obtained by the Maxwell relation.


Results and Discussions
Structure, morphology and mechanical properties. Mn 0.66 Fe 0.34 Ni 0.66 Fe 0.34 Si 0.66 Ge 0.34 precursor is prepared by the method mentioned in ref. 12 . The room-temperature powder X-ray diffraction (XRD) measurement ( Fig. 1a) indicates the coexistence of O and H phases, suggesting that the H-O structural transformation in Mn 0.66 Fe 0.34 Ni 0.66 Fe 0.34 Si 0.66 Ge 0.34 precursor occurs at around RT. It agrees with the results in ref. 12 and is also proved by differential scanning calorimetry (DSC) measurement in this work (shown in Fig. S1 in Supplementary information). With the occurrence of H-O structural transformation, the precursor breaks itself into small particles with an average size of ~700 μm. Before synthesizing the Mn 0.66 Fe 0.34 Ni 0.66 Fe 0.34 Si 0.66 Ge 0.34 /Sn composite, these particles were ground into powders. The size of obtained powders ranges from 2 to 30 μm with an average value of 9.94 μm (Fig. 1b). This value was obtained by counting all the powders in the micrograph shown in the inset of Fig. 1b. As the particle size of the precursor is much larger than that of the ground powders, we call the precursor as "bulk" thereafter.
The Mn 0.66 Fe 0. 34 34 to Sn can be calculated, which is 1.02:1, 2.03:1 and 3.05:1 for S11, S21 and S31, respectively. The composites are 13 mm in diameter and 4 mm in height, and can be processed into the cuboid shape with a size of 3.5 mm × 3.7 mm × 7.3 mm by a diamond wire saw (the inset of Fig. 1c). It is notable that if the weight ratio of Mn 0.66 Fe 0.34 Ni 0.66 Fe 0.34 Si 0.66 Ge 0.34 :Sn is higher than 3:1 or the processing is performed without pressure, the composites with special shapes cannot form. The XRD patterns of the composites (Fig. 1a Fig. 1d-f. The elemental mapping images (the  Table 1. The magnetostructural transformation in the bulk occurs at around RT, which agrees well with the XRD data. After grinding the bulk into powders, the magnetostructural transformation temperature doesn't shift obviously, but the transformation width (W) becomes broad. It can be attributed to the so-called "particle size effect" 11 . The transformation widths in the cooling and heating processes are calculated by W(Cooling) = M s − M f and W(Heating) = A f − A s , respectively (listed in Table 1). With embedding the powders into the Sn matrix, the values of M s , M f , A s , A f of the composites slightly increase compared with those of the powders, and it  can be attributed to the diffusion of Ge atoms into Sn matrix (see Fig. S2 and the corresponding statement in Supplemental information). The M-T curves measured under 5 T (Note that the magnetic field of 5 T is high enough to saturate the ferromagnetic O-phase 12 ) are shown in Fig. 2b. Sorting by the saturation magnetization in the low-temperature ferromagnetic phase, the order is the bulk, powders, S31, S21 and S11. As mentioned before, the particle size ranges from 2 to 30 μm after grinding. Due to the so-called size effect 11 , the particles with the size smaller than 5 μm lose the ability of structural transformation and keep at the stable hexagonal phase.
Since the Curie-temperature of hexagonal phase is around 200 K 12 , these particles are paramagnetic in the measurement temperature region. Therefore, the magnetization of low-temperature phase in the powder under 5 T is lower than that of the bulk (Fig. 2b). In the composite, the powders are mixed with diamagnetic Sn. In that case, the magnetization of low-temperature phase further decreases with increasing Sn content (Fig. 2b). According to Fig. 2b,  According to the Clausius-Clapeyron relation, due to the existence of ΔM between the O and H phases, the magnetostructural transformation in MnMX system can be induced by the magnetic field. The magnetic field-induced magnetostructural transformation manifests as the shift of transformation temperature when applying magnetic field. Taking S31 for instance, the magnetostructural transformation shifts to the higher temperatures with the increase of applied magnetic field, suggesting the magnetic-field-induced magnetostructural transformation (Fig. 2c). This effect can be clearly described when normalizing the curves by  Table S1 in Supplementary information). It can be found that the values of R of the powders and composites are larger than that of the bulk. The magnetic-field-induced magnetostructural transformation can be understood as a process that the grains with H-structure overcome some constraints and transform to O-structure when introducing magnetic field energy. In the bulk, due to the large volume difference between O and H structures, the grains with different structures restrain each other. Therefore, compared with the residual strain and defects, the stress generated from the interfaces between grains is the dominant constraint on the structural transformation 11 . With grinding the bulk into powders, the grains are separated from each other and the interfaces are reduced. So the dominant constraint is largely released in the powders and it becomes much easier to induce the H-O structural transformation by the magnetic field than that in the bulk. But when embedding the powders into the Sn matrix, the occurrence of magnetic-field-induced structural transformation needs to overcome the additional constraint applied by Sn. Therefore, R of the composites is smaller than that of the powders, but is still almost twice as large as that of the bulk.

Magnetocaloric effect.
Accompanied by the magnetic-field-induced structural transformation, the magnetocaloric effect can be obtained. In this work, the magnetocaloric effect is estimated by a simple model based on the entropy-temperature (S-T) diagram, which is also mentioned in ref. 35 . In this model, the S-T diagram is built by drawing the tangent lines at the inflection points of the two entropy curves in zero field and an applied magnetic field, thus the area in the diagram is a parallelogram. As shown in Fig. 3, the black solid and dotted lines represent the temperature-dependent entropy under zero field and applied magnetic field, respectively. M s (B) and M f (B) are the martensitic start and finish temperatures under a magnetic field of B. The entropy change of complete transformation (L) (also called the latent heat) is determined from the DSC data (shown in Fig. S1) by M M baseline 1 f s where  Q is the heat flow per mass unit and Q  baseline can be obtained by adjusting a smooth line at temperatures below and above the transition anomalies 36 . The calculated L of the bulk, powders and composites are also listed in Table 1. The isothermal entropy change (ΔS) and adiabatic temperature change (ΔT ad ) can be obtained by measuring the length of the perpendicular and horizontal arrows indicated in Fig. 3. According to the geometrical proportions, it can be found that the maximum ΔS (ΔS max ) will appear in the temperature range between M f (B) and M s . The ΔS max and ΔT ad can be linked by So the obtained ΔS max is determined by the latent heat, the rate of transformation temperature shift by magnetic field and transformation width. When W is lower than the shift of entropy curves under the applied magnetic field, the ΔS max should be just equal to L, because the magnetic field can induce a complete transformation in this temperature region. Based on this, the ΔS max should be written as following: In the condition of ΔB = 5 T, W is still larger than R·ΔB for all our composite samples. Therefore, the values of ΔS max (0-5 T) can be calculated by Eq. 6 using the data listed in Table 1, and they are −37.69, −22.40, −14.44, −13.16 and −10.76 J·kg −1 ·K −1 for the bulk, powder, S31, S21 and S11, respectively. According to the M-T curves under different magnetic fields, the Maxwell relation is also used to confirm the ΔS max (0-5 T). As shown in Fig. 4a, the corresponding values are −44.28, −18.97, −13.43, −11.10 and −9.02 J·kg −1 ·K −1 , which are in accordance with that calculated by Eq. 6. Based on the model and experimental data, the mean values and standard deviation are calculated (shown in the Fig. 4b). It also indicates a good accordance. Sorting by the largest magnetic entropy change, the order is the bulk, powder, S31, S21 and S11. After grinding the bulk into powder, W increases (see Table 1). It leads to the reduced ΔS max because there is an inverse relationship between ΔS max and W. On the other hand, the fraction of particles with stable phase causes a decrease of L in per unit mass, which also leads to the reduced ΔS max . Although R is increased, it is not high enough to prevent the decrease of ΔS max . With embedding the powder into Sn, R and W don't change obviously (see Table 1), but the L is reduced because of the existence of Sn. Therefore, ΔS max further decreases as Sn-content increases. Although ΔS max is reduced, the composites exhibit an improved machinability. On the other hand, the values of full width at half maximum for S31, S21 and S11 are 12.72, 11.43 and 12.55 K, which are larger than that of the bulk (7 K), indicating the broadened operating temperature range.
Additionally, the observed thermal hysteresis in composite is higher than 20 K and the shift of transformation temperature in a reasonable magnetic field is relatively lower than that in the other magnetic-transition alloys, such as La(Fe,Si) 13 and MnFe(P,Si) alloys [25][26][27]31,37 . In that case, the magnetic-field-excited orthorhombic phase maintains after the field is removed, and no metamagnetic transition occurs during the second field cycle. Thus, the magnetocaloric effect is nearly zero in cycling condition. The irreversibility of magnetocaloric effect hinders its application as magnetic cooling refrigerant. To enhance the reversibility, how to greatly reduce the thermal hysteresis and increase the rate of the transformation temperature shift by magnetic field is the question that is worth thinking about.

Conclusions
In summary, the Mn 0.66 Fe 0. 34  grains, the composites exhibit a broadened magnetostrutural transformation and an improved rate of the transformation temperature shift by magnetic field relative to those of the bulk. Accompanied by the occurrence of magnetic-field-induced magnetostructural transformation, these composites exhibit magnetocaloric effect. The isothermal entropy change is calculated by a simple model based on S-T diagram. The obtained results are consistent with that obtained by Maxwell relation.

Methods
The Mn 0.66 Fe 0.34 Ni 0.66 Fe 0.34 Si 0.66 Ge 0.34 precursor was prepared by the method mentioned in ref. 12 . For synthesizing the Mn 0.66 Fe 0.34 Ni 0.66 Fe 0.34 Si 0.66 Ge 0.34 /Sn composite, the precursor alloy was ground into powders using a ceramic mortar by hand, and then mixed with the commercial Sn powders with an average size of 43 μm for one more hour grinding using an agate mortar. The mixed powders were hot-pressed at 280 °C under 250 MPa for 5 min in vacuum and then slowly cooled to RT in 6 hrs. The applied pressure is maintained till the sample is cooled to RT.
The structural transition was investigated by DSC (Mettler Toledo, DSC 3) with a ramp rate of 10 K/min. The structural characterization was performed by XRD (Bruker, D8 Advance) at RT with Cu-Ka radiation. The cross-sectional microstructure was observed by SEM (FEI Quanta 250F). The elemental mapping image was obtained by energy-dispersive spectroscopy (FEI Quanta 250F). The M-T curve was carried out using a Physical Property Measurement System (Quantum Design, Dynacool) with a ramp rate of 2 K/min. The yield compressive strength was tested by an universal testing machine. The thermal expansion was investigated by thermomechanical analysis (402 F3 Hyperion). Data availability. All relevant data are available from authors upon reasonable request.