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Article

Strain Engineering in Ni-Co-Mn-Sn Magnetic Shape Memory Alloys: Influence on the Magnetic Properties and Martensitic Transformation

by
Qinhan Xia
1,
Changlong Tan
1,2,*,
Binglun Han
1,
Xiaohua Tian
3,*,
Lei Zhao
2,
Wenbin Zhao
2,
Tianyou Ma
1,
Cheng Wang
1 and
Kun Zhang
1,2,4,*
1
School of Science, Harbin University of Science and Technology, Harbin 150080, China
2
School of Materials Science and Chemical Engineering, Harbin University of Science and Technology, Harbin 150080, China
3
School of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China
4
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
*
Authors to whom correspondence should be addressed.
Materials 2022, 15(17), 5889; https://doi.org/10.3390/ma15175889
Submission received: 16 July 2022 / Revised: 17 August 2022 / Accepted: 23 August 2022 / Published: 26 August 2022
(This article belongs to the Special Issue Phase Transformation, Functional Properties, and Crystallography of Advanced Materials)
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Abstract

:
Ni-Mn-Sn ferromagnetic shape memory alloys, which can be stimulated by an external magnetic field, exhibit a fast response and have aroused wide attention. However, the fixed and restricted working temperature range has become a challenge in practical application. Here, we introduced strain engineering, which is an effective strategy to dynamically tune the broad working temperature region of Ni-Co-Mn-Sn alloys. The influence of biaxial strain on the working temperature range of Ni-Co-Mn-Sn alloy was systematically investigated by the ab initio calculation. These calculation results show a wide working temperature range (200 K) in Ni14Co2Mn13Sn3 FSMAs can be achieved with a slight strain from 1.5% to −1.5%, and this wide working temperature range makes Ni14Co2Mn13Sn3 meet the application requirements for both low-temperature and high-temperature (151–356 K) simultaneously. Moreover, strain engineering is demonstrated to be an effective method of tuning martensitic transformation. The strain can enhance the stability of the Ni14Co2Mn13Sn3 martensitic phase. In addition, the effects of strain on the magnetic properties and the martensitic transformation are explained by the electronic structure in Ni14Co2Mn13Sn3 FSMAs.

1. Introduction

Ni-Mn-Sn ferromagnetic shape memory alloys (FSMAs) with various related magnetic effects, including excellent magnetocaloric effect (MCE) [1,2], extraordinary magnetic shape memory effect (MSME) [3,4,5], and magnetoresistance effect (MR) [6,7]. These multifunctional properties are attributable to the coupling between the magnetic and structural transitions by the magnetic field [8,9,10], i.e., magnetic field-induced martensitic transformation (MFIMT). It is the magnetic field-driven shape memory behavior that makes ferromagnetic shape memory alloys different from conventional shape memory alloys, which must be actuated through temperature. The application of magnetic fields is fast and easy, and its fast response to magnetic fields makes this alloy more widely used than conventional shape memory alloys. Moreover, Ni-Mn-Sn FSMAs are cheap, non-toxic, and have simple fabrication processes, which highlights their advantages over conventional shape memory alloys. Although Ni-Mn-Sn FAMAs have so many excellent properties, the relatively narrow working temperature range is still a key drawback in extensive practical application [11,12]. Previous studies have pointed out that the narrow working temperature of Ni-Mn-Sn alloys is mainly near room temperature or slightly below it [13,14,15,16,17,18,19,20], which is just more beneficial to magnetic solid-state refrigeration. However, for the automotive, manufacturing, and energy exploration industries, the high working temperature region of the alloys is needed [21,22]. Similarly, a working temperature range lower than 270 K is needed for several space solutions [23]. In addition, the working temperature is very sensitive to constituent elements. That is, the working temperature region with fixed components is also fixed, which also increases the difficulty of widening the working temperature region. Therefore, obtaining the adjustable working temperature range is an urgent problem to be solved in Ni-Mn-Sn alloys.
Strain engineering is an efficient method to enhance the properties of functional materials [24,25,26,27]. Experimentally, Huang et al. found that uniaxial strain will be an effective means to control thermal effects (such as giant MCE and elastocaloric effects). A significant cooling level of about 4 K is measured when the strain is released [28]. Yang et al. observed that the martensitic transformation temperature (TM) increased with the increase in uniaxial strain in Ni43.5Co6.5Mn39Sn11 [29]. In addition, Zhao et al. also measured that the refrigerating temperature region increased by 6 K to 10 K in Ni43Co7Mn39Sn11 films with applying strain [30]. It can be seen that stress engineering is a very effective method to improve many properties of the system. However, few studies have been able to draw on any systematic research on the influence of biaxial strain on the working temperature in the Ni-Mn-Sn system.
The stable MFIMT and the dynamical working temperature are necessary for a tunable broad working temperature region in Ni-Mn-Sn. For a stable MFIMT, the alloys must be ferromagnetic in the austenitic phase (FM) and antiferromagnetic in the martensitic phase (AF) for a stable MFIMT (AFM). For the dynamical working temperature, the alloys need to require two conditions. (1) Both TM and Curie temperature (TC) need to be dynamic. (2) Keeping TM lower than TC. In addition, from the view of calculations, the large magnetization (ΔM) between the austenitic and martensitic phases is beneficial to the stable MFIMT [5]. The total energy difference (ΔEA-M) between the austenitic phase and martensitic phase and the total energy difference (ΔEP-F) between the ferromagnetic austenitic phase and paramagnetic austenitic phase play important roles in predicting the working temperature in alloys [5,31,32]. The TM and TC are increasing with the increase in the ΔEA-M and ΔEP-F, respectively [31,33]. In light of this, we calculated the ΔM, ΔEA-M, and ΔEP-F with the different strains through first-principles calculations. The results show that the value of ΔM of Ni-Mn-Sn alloys is too small to meet the stable MFIMT. Thus, to improve the value of ΔM and ΔEP-F, we choose the method of doping elements (Co to substitute for Ni atoms) [34,35]. In this way, Ni-Co-Mn-Sn alloys not only have a stable MFIMT but also have a dynamic working temperature. It is a high-quality candidate material for dynamically adjusting the working temperature region.
In the present paper, we aim to propose a strategy to adjust the broad working temperature of Ni-Co-Mn-Sn alloys by strain (from 200 K to 370 K). By using the first-principles calculation, the influences of strain on the magnetic properties, the martensitic phase transformation (MPT), and the working temperature of the alloys have been comprehensively studied. According to the results, a small strain can significantly change the working temperature and maintain the stable MFIMT, and the wide working temperature region of 168 K to 330 K can be predicted under strain from 0% to −1.5% in Ni14Co2Mn13Sn3 alloys. In addition, we discussed the physical mechanism of magnetic and martensitic transformation of the Ni14Co2Mn13Sn3 alloy through the electronic structure.

2. Calculation Method

The Vienna Ab initio Simulation Package (VASP) code is used to reveal the magnetic properties [36,37], phase structures, and electronic structures of Ni-Co-Mn-Sn FSMAs. All works were performed on the basis of the density functional theory (DFT). As the exchange–correlation functional, we used the Perdew–Burke–Ernzerhof (PBE) method and the generalized gradient approximation (GGA) [38]. For Ni-Mn-Sn FSMAs, a k-mesh of 3 × 6 × 6 is used for two phases. The cut-off energy is 500 eV. The L21 austenite structure ( F m 3 ¯ m ) of Ni16Mn13Sn3 with three inequivalent Wyckoff positions (4a, 4b, 8c) is shown in Figure 1a. The Sb and Mn atoms occupy 4a (0, 0, 0) and 4b (0.50, 0.50, 0.50) positions respectively and Ni atoms occupy the 8c ((0.25, 0.25, 0.25) and (0.75, 0.75, 0.75)) sites. In addition, the calculation method used in the transformation process from austenite to martensite is tetragonal distortion. That is, on the premise of keeping the cell volume unchanged, the optimized austenite structure is subjected to lattice distortion with different tetragonal distortion rates c/a so as to obtain the most stable martensite structure. As seen in Figure 1b, we substituted Co atoms for Ni atoms directly in our study, and MnSn is the designation for the excess Mn atoms at the deficient Sn atoms. The Mn atoms that remain at their sites are called MnMn in the Ni16−xCoxMn13Sn3 (x = 0, 1, 2) FSMAs. For both the austenitic and martensitic phases, we calculated two situations: the magnetic properties of Ni16−xCoxMn13Sn3 (x = 0, 1, 2) alloys are FM states and AFM states. The FM configuration was set by magnetic moments of all Mn atoms (MnSn and MnMn) parallel to each other. AFM configuration was decided by magnetic moments of MnSn, which are opposite in the direction of the magnetic moments of the MnMn. According to the VASP user manual [39], the calculation of spin polarization requires the parameter ISPIN = 2, while the setting of FM and AFM is determined by the parameter MAGMOM. Therefore, the spin polarization of both ferromagnets and antiferromagnets can be achieved by VASP. In first-principles calculations, we simulate biaxial strain by changing lattice vectors directly. That is, fixing the lattice constant in the c-axis while relaxing the lattice constants in the a-axis and b-axis. It is worth mentioning that 0% represents no deformation, positive deformation represents stretching, and negative deformation represents compression.

3. Results and Discussions

First, we investigated the two phasic structures, martensitic transition and magnetic properties of the Ni16Mn13Sn3. Table 1 shows the results of our calculations for the magnetic properties and equilibrium lattice parameters of the Ni16Mn13Sn3 alloys. For the Ni16Mn13Sn3 austenitic phase, the AFM state of the alloy is low energy, and the equilibrium lattice parameter is 5.94 Å. The magnetic ground state and lattice constant are in good agreement with other theoretical values [40]. In the Ni16Mn13Sn3 martensitic phase, the FM state has higher energy and is more unstable than the AFM state at c/a~1.35. That is, austenite and martensite phase are AFM states under 0% strain. This is also consistent with the theoretical results [3]. According to the energy corresponding to 0% strain in Figure 2, the energy of AFM austenite is higher than that of AFM martensite, so MPT will occur, which is a prerequisite for shape memory alloys. This is also verified experimentally [41]. The above results confirm the correctness of our calculation, so we can apply biaxial strain based on it, and then we calculated the total energies E of the Ni16Mn13Sn3 austenitic phase and martensitic phase with strain (−1.5~1.5%), as shown in Figure 2a,b respectively, to reveal the effect of strain on the phase structures, MPT, and magnetic properties. Figure 2a indicates that the energy of the AFM state is lower than that in the FM state for the austenite phase, and the total energies E of Ni16Mn13Sn3 austenitic phase firstly decrease with strain from 1.5% to 0% and then increase with strain from 0% to −1.5%. For the Ni16Mn13Sn3 martensitic phase, the total energy E of both FM and AFM increases with strain from 1.5% to −1.5%, and the AFM state energies are lower than the FM state energies. Therefore, we can conclude that austenite and martensite of Ni16Mn13Sn3 alloy are still in AFM state under the application of biaxial strain; that is, the biaxial strain will not affect the magnetic ground state of the system. In addition, the value of ΔEA-M and ΔEP-F in Ni16Mn13Sn3 alloys under strain (−1.5~1.5%) are shown in Figure 3 to show the impact of strain on TM and TC. It is obvious that the ΔEA-M increases with strain, while the ΔEP-F decrease with strain under strain from 1.5% to −1.5%. This shows that TM and TC increase with the increase in ΔEA-M and ΔEP-F, respectively. According to the results, applying strain can tune the working temperature of Ni16Mn13Sn3 alloys. Based on the above results, it can be concluded that the stability of austenite will be reduced no matter whether biaxial compressive strain or biaxial tensile strain is applied. However, the stability of martensite increases with compressive strain and decreases with tensile strain. Moreover, the biaxial strain does not affect the occurrence of MPT and the most stable magnetic configuration of each phase.
In order to tune the working temperature of alloys, alloys must have stable MFIMT. The ΔM is larger, and the MFIMT is more stable [41,42]. Therefore, we calculated the ΔM of Ni16Mn13Sn3 alloys with strain in Table 1. Table 1 further accurately shows that the ΔM of Ni16Mn13Sn3 is very small, and the strain has a weak effect on the value of ΔM (0.06–0.01 μB). The low ΔM cannot satisfy the stable MFIMT. Therefore, the biaxial strain alone cannot satisfy the stable MFIMT, which is a necessary condition for an adjusted wide working temperature region. Fortunately, the Co element enhances ferromagnetism in the austenitic phase and TC of Ni16Mn13Sn3 alloys. Thus, the strain may be an efficacious strategy to adjust the wide working temperature of Ni-Co-Mn-Sn.
The impact of Co doping on the physical properties of the Ni-Co-Mn-Sn system, particularly on the operating temperature, must also be taken into account. We first evaluate the equilibrium lattice parameters and magnetic properties of the Ni16−xCoxMn13Sn3 (x = 1, 2) and present them in Table 1 to show the change in phase structures, MPT, and magnetic properties of the Ni16Mn13Sn3 with Co doping. The findings demonstrate that as Co increases, the equilibrium lattice parameters of the Ni16−xCoxMn13Sn3 (x = 1, 2) austenitic phases increase from 5.91 Å to 5.93 Å. The change of Ni16−xCoxMn13Sn3 (x = 1, 2) lattice constant can be attributed to the fact that the atomic radius of the substitution elements is slightly larger than that of the substituted element, and the lattice parameters are close to the value of the experiment (5.987 Å) and theory (5.973 Å) [43,44]. The origin of the experimental error is the slight difference between the actual compound and the nominal compound, and then the DFT calculation is carried out at T = 0 K, while the equilibrium lattice constant measured by XRD is carried out at room temperature. The theoretical error may be caused by the error between different calculation software. The austenitic Ni14Co2Mn13Sn3 phase is the FM state, whereas the martensitic phase is the AFM state, and there is a large ΔM (5.48 μB) between these two phases as shown in Table 1. This is also consistent with the experimental facts (6.68 μB) [45]. In short, the Ni14Co2Mn13Sn3 alloys meet the stable MFIMT, and the strain method may be an efficient strategy to tune the wide working temperature of Ni14Co2Mn13Sn3 alloys.
Subsequently, we calculated the total energies of Ni14Co2Mn13Sn3 alloys with strain (−1.5~1.5%) and shown in Figure 4 to show the impact of the magnetic properties and working temperature on this alloy. It is obvious that the total energies of austenitic phases firstly decrease with strain (−1.5~0%) and then increase with strain (0–1.5%), and FM states are the most stable magnetic configuration for austenitic phases. The total energies of martensitic phases increase with strain (−1.5~1.5%), as shown in Figure 4b. Moreover, the most stable magnetic configuration of martensitic phases is AFM states. Combined with (a) and (b) of Figure 4, it can be seen that the energy of AFM martensite is always less than that of FM austenite under the action of biaxial strain. It shows that the alloy will undergo magnetic structure coupling transformation, which further confirms that there is a large magnetic moment difference in the system. To show the change of TM and TC of Ni14Co2Mn13Sn3 alloys with strain, we listed the ΔEA-M and ΔEP-F in Table 2. The value of ΔEA-M increase with strain from 1.5% to −1.5%, while the value of ΔEP-F decrease with strain from 1.5% to −1.5%. The results show the strain can increase TM and decrease TC. In consideration of the wide working temperature of Ni14Co2Mn13Sn3 alloys, one of the conditions is that TC must be higher than TM. Therefore, we need to evaluate the value of TM and TC. Generally, the TM and TC increase linearly with ΔEA-M and ΔEP-F in Ni-Mn-based Heusler alloys. To further explore the relationship between TM and ΔEA-M, as depicted in Figure 5, we made the TM and ΔEA-M fitting curves [1,10,34,35,46,47,48,49,50,51]. According to the Heisenberg model and Stoner theory [52], the relationship of TM and ΔEA-M is represented by ΔEP-F = −kBTcM/M0, where M is the magnetic moment at T ≠   0 K, and M0 is the equilibrium magnetic moment at T = 0 K [53]. Based on it, we calculated the TM and TC of Ni14Co2Mn13Sn3 alloys with strain in Figure 6. It shows that the TM and TC increase with strain, and the TM is lower than TC with strain (−1.5~1.5%), which indicates that the alloy has been fully qualified to dynamically adjust the wide working temperature range. In addition, the changing trend of TM is consistent with the experiment in other Ni-Mn based [54]; that is, the working temperature moves to a high temperature under the compressive strain. Then, with strain from 0% to −1.5%, the Ni14Co2Mn13Sn3 FSMAs show a tunable wide working temperature (from 168 K to 330 K), which meets the application in different temperatures. The operating temperature range of Ni14Co2Mn13Sn3 is 160 K; the wide range may be overestimated compared to experimental values. In short, the strain method is an effective way to tune effectively by using the strain approach for Ni14Co2Mn13Sn3 alloys.
The total density of states (TDOS) of austenite and martensite in Ni14Co2Mn13Sn3 and the partial density of states (PDOS) of MnMn and MnSn of austenite and martensite in Ni14Co2Mn13Sn3 are shown in Figure 7, Figure 8 and Figure 9 respectively to further illuminate the physical mechanism of the MPT and magnetic properties [55,56]. In addition, the phase stability is strongly dependent upon the TDOS at the Fermi level plays (EF) [57,58]. Usually, the low TDOS indicates the stable phase in Ni14Co2Mn13Sn3 FSMAs. Figure 7a shows that the TDOS at EF of strain (−1.5%, 1.5%) is similar in Ni14Co2Mn13Sn3 austenitic phases. The strain has a weak effect on austenitic phase stability. Moreover, for martensitic phases, the TDOS of −1.5% strain is lower than the TDOS of 1.5% strain at EF, as shown in Figure 7b. The -1.5% strain decreases the instability of the Ni14Co2Mn13Sn3 martensitic phase. Then, the instability of the martensitic phase decreases, and the stability of austenitic phases show a few changes. In addition, austenite is a peak at EF, while martensite is a pseudopotential valley. It shows that the stability of austenite is lower than that of martensite, which leads to the MPT according to the Jahn teller splitting effect. The results show that strain can tune the TM of Ni14Co2Mn13Sn3 FSMAs.
For the magnetic properties of Ni14Co2Mn13Sn3 austenitic phases, as can be seen in Figure 8b, the PDOS of MnMn and MnSn are similar and mostly up-spin states under the EF. With applying strain, for Figure 8a,c, the PDOS of MnMn and MnSn has almost no change. This is indicated that the most stable magnetic configuration of austenitic phases is always FM, and this configuration is unaffected by strain. For martensite, in Figure 9b, the MnMn is in up-states while the MnSn is in down-states. With applying strain, the distribution of the PDOS of MnMn and MnSn is still different, the MnSn is down-state, but the MnMn is up-state, as shown in Figure 9a,c. The most stable magnetic configuration of martensite phases is AFM. In addition, the difference in the distribution of austenite and martensite also explains the existence of large ΔM. In conclusion, the strain cannot change the magnetic properties of Ni14Co2Mn13Sn3 FSMAs. The Ni14Co2Mn13Sn3 FSMAs meet the condition of the stable MFIMT.

4. Conclusions

To summarize, to achieve the tunable broad working temperature region of Ni-Mn-Sn alloys, we have systematically studied the influence of strain on the structures, MPT, and magnetic properties Ni16−xCoxMn13Sn3 (x = 0, 1, 2) by first-principles calculation. The value of ΔEA-M increases with the strain from 1.5% to −1.5%, bringing about TM enhancement. According to the results, the strain method can reveal the ability of the tunable wide working temperature range in Ni14Co2Mn13Sn3 FSMAs. Particularly, with a slight strain (0~1.5%), Ni14Co2Mn13Sn3 with a large working temperature region of ~160 K and the working temperature (168–330 K) of Ni14Co2Mn13Sn3 satisfy the application from low-temperature to high-temperature. This work predicts an adjusted broad working temperature region of Ni-Mn-Sn alloys, which shows a great application range of Ni-Mn-Sn FSMAs. Therefore, the strain method provides the reference for designing the tunable wide working temperature FSMAs and makes it possible for the wide application of FSMAs.

Author Contributions

Conceptualization, K.Z.; Data curation, B.H.; Software, L.Z., W.Z., T.M. and C.W.; Writing–original draft, Q.X.; Writing–review & editing, C.T., X.T. and K.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 51971085, 51871083, 52001101) and the China Postdoctoral Science Foundation (Grant No. 2021M693229).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

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Materials 15 05889 g001 550
Figure 1. (a) Crystallographic structure in Ni16Mn13Sn3 austenitic phase. (b) Crystallographic structure in Ni15CoMn13Sn3 austenitic phase.
Figure 1. (a) Crystallographic structure in Ni16Mn13Sn3 austenitic phase. (b) Crystallographic structure in Ni15CoMn13Sn3 austenitic phase.
Materials 15 05889 g001
Materials 15 05889 g002a 550Materials 15 05889 g002b 550
Figure 2. Strain change (−1.5~1.5%) of the total energies of Ni16Mn13Sn3 alloys. (a) the austenitic phase. (b) the martensitic phase.
Figure 2. Strain change (−1.5~1.5%) of the total energies of Ni16Mn13Sn3 alloys. (a) the austenitic phase. (b) the martensitic phase.
Materials 15 05889 g002aMaterials 15 05889 g002b
Materials 15 05889 g003 550
Figure 3. Strain change (−1.5–1.5%) of ΔEA-M and ΔEP-F for Ni16Mn13Sn3.
Figure 3. Strain change (−1.5–1.5%) of ΔEA-M and ΔEP-F for Ni16Mn13Sn3.
Materials 15 05889 g003
Materials 15 05889 g004 550
Figure 4. Strain change (−1.5~1.5%) of the total energies of Ni14Co2Mn13Sn3 alloys. (a) The austenitic phase. (b) the martensitic phase.
Figure 4. Strain change (−1.5~1.5%) of the total energies of Ni14Co2Mn13Sn3 alloys. (a) The austenitic phase. (b) the martensitic phase.
Materials 15 05889 g004
Materials 15 05889 g005 550
Figure 5. Relationship of ΔEA-M and experimental TM of alloys.
Figure 5. Relationship of ΔEA-M and experimental TM of alloys.
Materials 15 05889 g005
Materials 15 05889 g006 550
Figure 6. Strain change (−1.5~1.5%) of the TM and the TC in Ni14Co2Mn13Sn3.
Figure 6. Strain change (−1.5~1.5%) of the TM and the TC in Ni14Co2Mn13Sn3.
Materials 15 05889 g006
Materials 15 05889 g007 550
Figure 7. Strain change (−1.5%, 1.5%) of the TDOS of Ni14Co2Mn13Sn3 alloys. (a) the austenitic phase. (b) the martensitic phase.
Figure 7. Strain change (−1.5%, 1.5%) of the TDOS of Ni14Co2Mn13Sn3 alloys. (a) the austenitic phase. (b) the martensitic phase.
Materials 15 05889 g007
Materials 15 05889 g008 550
Figure 8. Strain change (−1.5%, 0%, 1.5%) of the PDOS of Ni14Co2Mn13Sn3 austenitic phase. (a) −1.5% strain, (b) 0% strain, (c) 1.5% strain.
Figure 8. Strain change (−1.5%, 0%, 1.5%) of the PDOS of Ni14Co2Mn13Sn3 austenitic phase. (a) −1.5% strain, (b) 0% strain, (c) 1.5% strain.
Materials 15 05889 g008
Materials 15 05889 g009 550
Figure 9. Strain change (−1.5%, 0%, 1.5%) of the PDOS of Ni14Co2Mn13Sn3 martensitic phase. (a) −1.5% strain, (b) 0% strain, (c) 1.5% strain.
Figure 9. Strain change (−1.5%, 0%, 1.5%) of the PDOS of Ni14Co2Mn13Sn3 martensitic phase. (a) −1.5% strain, (b) 0% strain, (c) 1.5% strain.
Materials 15 05889 g009
Table
Table 1. Equilibrium lattice parameters, total spin moments and magnetic state of the cubic austenite (Cub.) and tetragonal non-modulated martensite (Tet.) for Ni16−xCoxMn13Sn3 (x = 0, 1, 2) alloys with strain (−1.5~1.5%).
Table 1. Equilibrium lattice parameters, total spin moments and magnetic state of the cubic austenite (Cub.) and tetragonal non-modulated martensite (Tet.) for Ni16−xCoxMn13Sn3 (x = 0, 1, 2) alloys with strain (−1.5~1.5%).
AlloysStrain
%		Phasea
Å		c
Å		Mt
μB		|ΔM|
μB		Magnetic State
FM/AFM
Ni16Mn13Sn3−1.5Cub.5.855.941.360.06AFM
Tet.5.307.261.42 AFM
−1.0Cub.5.885.941.370.05AFM
Tet.5.337.261.42 AFM
−0.5Cub.5.915.941.380.04AFM
Tet.5.357.261.42 AFM
0Cub.5.945.941.390.04AFM
Tet.5.387.261.43 AFM
0.5Cub.5.975.941.400.03AFM
Tet.5.417.261.43 AFM
1.0Cub.6.005.941.410.02AFM
Tet.5.437.261.43 AFM
1.5Cub.6.035.941.420.01AFM
Tet.5.467.261.43 AFM
Ni15CoMn13Sn3−1.5Cub.5.835.921.420.02AFM
Tet.5.357.061.44 AFM
−1.0Cub.5.865.921.440.01AFM
Tet.5.377.061.45 AFM
−0.5Cub.5.895.921.440.01AFM
Tet.5.407.061.45 AFM
0Cub.5.925.921.460AFM
Tet.5.437.061.46 AFM
0.5Cub.5.955.921.470AFM
Tet.5.467.061.47 AFM
1.0Cub.5.985.921.490.01AFM
Tet.5.487.061.48 AFM
1.5Cub.6.015.921.500.01AFM
Tet.5.517.061.49 AFM
Ni14Co2Mn13Sn3−1.5Cub.5.845.936.985.48FM
Tet.5.327.151.50 AFM
−1.0Cub.5.875.937.005.50FM
Tet.5.357.151.50 AFM
−0.5Cub.5.905.937.035.51FM
Tet.5.377.151.52 AFM
0Cub.5.935.937.065.54FM
Tet.5.407.151.52 AFM
0.5Cub.5.965.937.085.56FM
Tet.5.437.151.52 AFM
1.0Cub.5.995.937.105.58FM
Tet.5.457.151.52 AFM
1.5Cub.6.025.937.135.58FM
Tet.5.487.151.55 AFM
Table
Table 2. Calculated energy difference ΔEA-M in meV/atom between the austenite and martensite phases, ΔEP-F in meV/atom between the paramagnetic and ferromagnetic state, martensite transition temperature TM and Curie temperature TC in Ni16−xCoxMn13Sn3 (x = 0, 1, 2) alloys with strain (−1.5~1.5%).
Table 2. Calculated energy difference ΔEA-M in meV/atom between the austenite and martensite phases, ΔEP-F in meV/atom between the paramagnetic and ferromagnetic state, martensite transition temperature TM and Curie temperature TC in Ni16−xCoxMn13Sn3 (x = 0, 1, 2) alloys with strain (−1.5~1.5%).
AlloysStrain
%		ΔEA-M (meV/atom)ΔEP-F (meV/atom)TM (K)TC (K)
Ni16Mn13Sn3−1.531.7385.7405397
−1.029.6387.8378399
−0.527.6390.0353401
024.6393.3314405
0.522.3395.2285407
1.019.4397.6248409
1.518.5400.7236412
Ni15CoMn13Sn3−1.530.8392.6394404
−1.028.1395.9359407
−0.526.8397.7343409
023.4398.2299410
0.521.6403.4276415
1.018.7407.3239419
1.517.8410.4227422
Ni14Co2Mn13Sn3−1.525.8399.6330411
−1.022.9402.1293414
−0.519.0404.8243416
013.2406.9168419
0.512.7410.7162423
1.09.8413.8125426
1.57.2415.792428
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Xia, Q.; Tan, C.; Han, B.; Tian, X.; Zhao, L.; Zhao, W.; Ma, T.; Wang, C.; Zhang, K. Strain Engineering in Ni-Co-Mn-Sn Magnetic Shape Memory Alloys: Influence on the Magnetic Properties and Martensitic Transformation. Materials 2022, 15, 5889. https://doi.org/10.3390/ma15175889

AMA Style

Xia Q, Tan C, Han B, Tian X, Zhao L, Zhao W, Ma T, Wang C, Zhang K. Strain Engineering in Ni-Co-Mn-Sn Magnetic Shape Memory Alloys: Influence on the Magnetic Properties and Martensitic Transformation. Materials. 2022; 15(17):5889. https://doi.org/10.3390/ma15175889

Chicago/Turabian Style

Xia, Qinhan, Changlong Tan, Binglun Han, Xiaohua Tian, Lei Zhao, Wenbin Zhao, Tianyou Ma, Cheng Wang, and Kun Zhang. 2022. "Strain Engineering in Ni-Co-Mn-Sn Magnetic Shape Memory Alloys: Influence on the Magnetic Properties and Martensitic Transformation" Materials 15, no. 17: 5889. https://doi.org/10.3390/ma15175889

APA Style

Xia, Q., Tan, C., Han, B., Tian, X., Zhao, L., Zhao, W., Ma, T., Wang, C., & Zhang, K. (2022). Strain Engineering in Ni-Co-Mn-Sn Magnetic Shape Memory Alloys: Influence on the Magnetic Properties and Martensitic Transformation. Materials, 15(17), 5889. https://doi.org/10.3390/ma15175889

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