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Twinning stress is known to be a critical factor for the actuating performance of magnetic shape memory alloys because of the harmful deterioration of their magnetic field-induced strain effect. However, the intrinsic origin of the high twinning stress is still in debate. In this work, we firstly fill this gap by precisely probing the reorientation behaviors of A-C and A-B two common macro-twin interfaces under the stimulus of uniaxial compression in-situ transmission electron microscope. The grain boundary is proved to be the main reason for large twinning stress. The twinning stress of the A-C and A-B type interfaces quantitatively are ∼0.69 and 1.27 MPa within the plate respectively. The A-C type interface evidently has smaller twinning stress and larger deformation variable than the A-B interface. Under the action of compression, not only the orientations of the crystals have changed, but also the roles of the major and minor lamellae have changed for both interfaces due to the movements of twinning dislocations. Combining in-situ and quasi in-situ electron diffraction data, the reorientation process is clearly and intuitively shown by the stereographic projection. Atomic models and the theory of dislocation motion are proposed to phenomenologically clarify the intrinsic mechanism. This work is believed to not only provide a deeper understanding of the deformation mechanism of magnetic shape memory alloys under uniaxial compression testing, but also discover that compression training is not the mechanical training way to decrease the twinning stress of non-modulated martensite in single crystal shape memory alloys.

Ni-Mn-based metamagnetic shape memory alloys (MSMAs) have excellent properties such as magnetic shape memory effect, giant magnetocaloric and barocaloric effects, magneto resistance, and exchange bias effects. These properties introduce them as potential novel materials for technological applications. Therefore, understanding and controlling the wear behavior of NiMn-based MSMAs is an important consideration for mechanical properties. In terms of technological applications, detailed tribological studies clarify the robustness in the harsh environment. In this study, we have performed the tribological behaviors of NiMnX (X = In and Sn) MSMAs. Additionally, the specified alloys are fabricated by two different methods to measure the effects of the fabrication method. The results showed that the wear testing and track depths are affected by fabrication methods, the contribution of X element, and wearing methods. The effect of the load is less significant for reciprocal sliding unlike to pin-on disk. For the pin-on disk, 5 N load presents a clear decrease by means of friction coefficient. Through the experiments, temperature changes from 24.3 to 48.6 °C. Microstructural evaluations highlighted that the alloys fabricated by induction furnace have lower width of wear track. Lastly, the NiMnSn alloy fabricated by using the arc melter comparatively has the widest wear track, 1303 µm.

Low twinning stress (TS) is a prerequisite for magnetic shape memory functionality in ferromagnetic martensites. We compare Ni50Mn28Ga22 (nominal at.%) single crystals from four different producers to reveal the effect of crystal quality on the TS. Near the reverse martensite transformation, the TS is generally low, about 1 MPa, regardless of mosaicity of up to 1.7° and chemical composition deviations of up to 2 at.% of Mn. Pure type I and type II twin boundaries occur in crystals with smooth chemical composition gradients. The corresponding temperature dependences of TS follow universal linear trends with the slopes of −0.045 MPa/K for type I twins and −0.001 MPa/K for type II twins, enabling a very low TS down to 2 K for the latter. An intermediate slope of −0.023 MPa/K appears for mixed type I/type II twin boundaries in a crystal with sharp local chemical deviations. We conclude that the crystal quality affects the magnitude of the TS indirectly, through its impact on the character of the twin boundaries. The effect is weak near the martensite transformation temperature and strong at low temperatures.

Heusler shape memory alloys are important for many applications due to their typical magnetic and shape memory behaviors. In this study, a Ni50Mn36Sn12Co2 (at.%) alloy was manufactured by arc-melting technique, then the ingot cooled to ambient temperature in the natural atmosphere. Three different temperatures, including 500 °C (773 K), 700 °C (973 K), and 900 °C (1173 K), was selected for aging the samples cut from the main ingot. The impact of aging on the crystalline; microstructure; caloric; and magnetic properties of the alloys were investigated through x-ray diffraction (XRD); scanning electron microscope; differential scanning calorimetric (DSC), differential thermal analysis, and thermal gravimetric (TG); and physical property measuring system was investigated, respectively. The aging in different temperatures led to the shift DSC curve, such that the martensitic phase transformation temperatures of the sample aged at 773 K increased, however, the transformation at 973 and 1173 K decreased compared to the as-casted alloy. The different phase transformation behavior showed that the alloy aged at 773 K has the maximum elastic energy, enthalpy and entropy change compared to the reset of samples, on the other hand, its crystallite sized obtained from XRD analysis comparably diminished. Besides, the TG analysis revealed that the mass gain almost occurs at a temperature above 773 K, therefore the magnetization of the alloys aged at 973 and 1173 K decreased due to a thin oxide layer formed on the surface of the alloys.

The composition dependence of the crystal structure and magnetism of the 6 M martensite for the Cu-doped Ni43.75Mn37.5In12.5Co6.25 alloy at different site occupations (Cu substitution for Ni, Mn, In, and Co, respectively) is investigated in detail with the first-principles calculations. Results show that the austenite (A) phase exhibits a ferromagnetic (FM) state in all occupation manners, the 6 M martensite possesses an FM state except for the case of Cu substitution at the normal Mn (Mn1) site, and the non-modulated (NM) martensite displays a ferrimagnetic (FIM) state apart from the Cu substitution at the Ni, Mn1, or In sites. The Cu atom destabilizes the A, 6 M, and NM phases regardless of the occupation manner. The one-step martensitic transformation from the A to NM phase occurs in the case of Cu substituting for Mn1, excess Mn (Mn2), or Co; for Cu substituting Ni, a martensitic transformation including 6 M martensite happens, i.e., A → 6 M → NM; however, the martensitic transformation disappears when Cu replaces In site. From the equilibrium lattice constants, it can be speculated that the substitution of Cu for Ni can effectively reduce the thermal hysteresis (∆THys). The magnetic properties are found to be greatly reduced by the substitution of the non-magnetic element Cu for the ferromagnetic Mn atom, whereas the effect is fewer in the remaining cases. It is predicted that the alloy has more favorable properties when Cu replaces Ni. The present results can lay a theoretical foundation for further development of multielement magnetic shape memory alloys.

Magnetic shape memory alloy-based actuator (MSMA-BA) has the capability to generate the micro–nano-scale precision positioning, which has unparalleled virtue in contrast with the traditional motion driving mechanism. Nevertheless, the output displacement of the MSMA-BA exhibits complex hysteresis nonlinearity, which hinders its utility in the high-precision positioning field. In this article, an online Volterra series model based on wavelet neural network (VSM-WNN) is proposed to describe the rate-dependent hysteresis of the MSMA-BA. The kernel function of the VSM is extracted with a WNN, in which the feasibility of this extraction is proved in theory via Taylor expansion of the wavelet function. Finally, the validity of the proposed model is confirmed by means of experiments. Experimental results indicate that the VSM-WNN has a remarkable performance in describing the traits of hysteresis behavior of the MSMA-BA.

The magnetic shape memory alloy (MSMA) is a new family of smart materials, which exhibits great strain deformation and high energy density. Based on these properties, the MSMA has excellent potential to represent an available means for developing a novel generation of actuators in the micro-positioning application. However, the MSMA-based actuator suffers from the inherent hysteresis and it has become a bottleneck in the industrial application. A hybrid hysteresis model, which consists of a simple dynamic hysteresis operator (SDHO) and chaotic neural network (CNN), is proposed in this article. This developed model possesses a concise construction and distinguished generalization capability. By conducting comparative experiments, the proposed approach has a superior ability to predict the hysteresis behaviors under various input signals.

The practical applications for the distinctive functions of metamagnetic Heusler alloys, such as magnetic shape memory effect, various caloric effects, etc., strongly depend on the phase transition temperatures. Here, flexible Heusler alloy Ni-Mn-Sn films have been deposited on mica substrates by pulsed laser deposition with a Ti buffer layer. Clear ferromagnetic (FM) transition followed by the martensitic transformation at around room temperature and exchange bias (EB) with a blocking temperature of 70 K are observed. Under the application of both tensile and compressive strains by bending the mica substrates, all the characteristic temperatures of Ni-Mn-Sn films, including the FM transition temperature, martensitic transformation temperature, and blocking temperature of EB, are significantly increased by about 10 K. Furthermore, EB field and coercivity are both strongly strengthened, which is mainly caused by the simultaneous enhancement of FM and anti-FM Mn-Mn coupling because of their shortened separations by strain and verified by the Monte Carlo simulation results. The strain controlling for structural and magnetic properties provides efficient manipulation for Heusler alloy-based magnetic devices.

Brittleness is a bottleneck hindering the applications of fruitful functional properties of Ni–Mn-based multiferroic alloys. Recently, experimental studies on B alloying shed new light on this issue. However, the knowledge related to B alloying is limited until now. More importantly, the mechanism of the improved ductility, which is intrinsically related to the chemical bond that is difficult to reveal by routine experiments, is still unclear. In this context, by first-principles calculations, the impact and the correlated mechanism of B alloying were systemically studied by investigating four alloying systems, i.e., (Ni2-xBx)MnGa, Ni2(Mn1-xBx)Ga, Ni2Mn(Ga1-xBx) and (Ni2MnGa)1-xBx. Results show that B prefers the direct occupation manner when it replaces Ni, Mn and Ga. For interstitial doping, B tends to locate at octahedral rather than tetrahedral interstice. Calculations show that the replacement of B for Ga can effectively improve (reduce) the inherent ductility (inherent strength) due to the weaker covalent strength of Ni(Mn)–B compared with Ni(Mn)–Ga. In contrast, B staying at octahedral interstice will lead to the formation of new chemical bonds between Ni(Mn) and B, bringing about a significantly improved strength and a greatly reduced ductility. Upon the substitutions for Ni and Mn, they affect both the inherent ductility and strength insignificantly. For phase transition, the replacement of B for Ga tends to destabilize the austenite, which can be understood in the picture of the band Jahn–Teller effect. Besides, the substitution for Ga would not lead to an obvious reduction of magnetization.

It is known from experimental findings that three-dimensional effects can have a strong influence on magnetic shape memory behavior. Such phenomena are, however, often neglected in MSMA constitutive models, as they only become meaningful under complex loading conditions. The extensions of our original modeling framework, cf. Bartel et al. (2020), to include 3D-effects is threefold: (i) vector-valued microstructural variables are now elements in R 3 , i.e. no longer parameterizable in polar coordinates, (ii) a third tetragonal martensite variant may form/vanish by switching from/back into both other variants, and (iii) a more general and robust algorithmic treatment is necessary. The latter includes the implementation of a staggered Augmented Lagrangian scheme to handle the now much larger and numerically more advanced sets of equality and inequality constraints. In this context, two extended model formulations are presented. The first considers a first-order, two-variant laminate approach (rank-one convexification), in which domain magnetizations, interface orientations etc. are now three-dimensional vectors. The second model is based on a convexification approach, for which the incorporation of the third martensitic variant is quite natural. Numerical examples are investigated to test the generalized modeling framework. Firstly, it is confirmed that both extended models recover the solution of the previously established two-dimensional model for a simple loading case. Secondly, response predictions for more complex loading scenarios (non-proportional bi-axial stresses, orthogonal magnetic field), motivated by experiments, are investigated. It is found that capturing the formation, elimination and mutual interaction of all martensitic variants as well as general three-dimensional magnetization vector orientations is of key importance under these conditions. The extended convexification model and modified algorithmic formulation are shown to reliably handle even such general cases.

In this paper, a common energy harvester is investigated which uses a specimen of magnetic shape memory alloy (MSMA). The aim of this study is to improve system performance and to evaluate the magneto-mechanical loading on the MSMA material. Since demagnetization effect is not included in the employed original MSMA model, a method to incorporate this effect is proposed which has a good performance for the specific magneto-mechanical loading of this problem. In order to decrease the need for bias magnetic field and increase system efficiency, a new return mechanism for the MSMA specimen is proposed. The results indicate that the maximum harvested power from the improved system is obtained at 0.55 T bias field, with 30% increase in power. Then, input mechanical loading in the system is studied. Firstly, applied strain rate caused by mechanical loading is studied, and a nonlinear relation between the induced RMS voltage and strain rate is observed. Next, 2D applied mechanical loading is investigated, and it is shown that by increasing the phase difference between mechanical loads in two directions, the induced voltage decreases. Moreover, applying dynamic effect to the model shows that for thin MSMA specimens, this effect is minor, but by increasing the thickness and loading frequency, the effect becomes tangible.

Magnetic soft materials (MSMs) have shown potential in soft robotics, actuators, metamaterials, and biomedical devices because they are capable of untethered, fast, and reversible shape reconfigurations as well as controllable dynamic motions under applied magnetic fields. Recently, magnetic shape memory polymers (M-SMPs) that incorporate hard magnetic particles in shape memory polymers demonstrated superior shape manipulation performance by realizing reprogrammable, untethered, fast, and reversible shape transformation and shape locking in one material system. In this work, we develop a multimaterial printing technology for the complex structural integration of MSMs and M-SMPs to explore their enhanced multimodal shape transformation and tunable properties. By cooperative thermal and magnetic actuation, we demonstrate multiple deformation modes with distinct shape configurations, which further enable active metamaterials with tunable physical properties such as sign-change Poisson's ratio. Because of the multiphysics response of the M-MSP/MSM metamaterials, one distinct feature is their capability of shifting between various global mechanical behaviors such as expansion, contraction, shear, and bending. We anticipate that the multimaterial printing technique opens new avenues for the fabrication of multifunctional magnetic materials.

This article investigates the basis for pressure sensor application based on the magnetic shape memory effect in membranes. Von Karmans nonlinear terms are considered in strain–displacement relationships of thin films, and a new method is presented for solution of large deflections of thin films with arbitrary boundary condition. In this study, the equations of motion of magnetic shape memory alloys are extended. In pressurized membranes, the complex distribution of mechanical stress can cause the martensitic reorientation, which is the underlying mechanism for sensing applications in magnetic shape memory alloys. To examine the obtained model, the governing equations of magnetic shape memory alloys are solved for clamped thin films and results are compared with experimental data. Demonstrating good agreement with experimental data, the presented model can be used for analysis of magnetic shape memory alloy–based smart structures. In this article, the deflection profile of the uniformly loaded thin films is determined with different boundary conditions. Furthermore, the center deflection of magnetic shape memory alloy membrane under different magnetic bias field is simulated. The results of simulation can be used for designing a membrane-based pressure sensor using magnetic shape memory alloys.

Magnetic shape memory alloy (MSMA), which has emerged in recent years, has been proven to have great potential for electromagnetic actuators due to the long life cycle, fast response, and relatively large load capacity. Current research on such material mainly focuses on the fundamentals, thermal effect, composition, and magnetic induction strain, but issues involved in its application to the industry are rarely addressed in detail. This article first analyzed the principle of magnetically induced strain and the corresponding constitutive equations, and investigated the magnetomechanical characteristics of the MSMA sample through measurement carried out on a specially designed experimental setup. Taking advantage of good drive performance, MSMA electromagnetic actuator with spring recovery was designed in detail. In order to resolve the contradiction between compactness and high magnetic field strength, a novel configuration with double-layered coils was proposed to achieve the required magnetic flux density. Influences of input current, prepressure, and spring stiffness on the dynamic response characteristics of the actuator excited by step signal and square wave signal input were analyzed by simulation. Finally, the experimental platform is built to verify the feasibility of the configuration and dynamic characteristics of the actuator. The experimental results show that the designed actuator has good output performance with a response time of 25 ms, demonstrating the superiority of MSMA in microdisplacement actuator with high dynamics.

The magnetic shape memory alloy (MSMA)-based actuator, as a new type of actuator, has a great application prospect in the micro-precision positioning field. However, the input-to-output hysteresis nonlinearity largely hinders its wide application. In this paper, a Takagi–Sugeno fuzzy neural network (TSFNN) model based on the modified bacteria foraging algorithm (MBFA) is innovatively utilized to describe the complex hysteresis nonlinearity of the MSMA-based actuator, and the parameters of TSFNN are optimized by the MBFA. The TSFNN is a combination of the fuzzy-logic system and neural network; thus, it has the capability of approximating the nonlinear mapping function and self-adjustment and is suitable for hysteresis modeling. The MBFA, which can obtain better optimization values, is employed for the parameter identification procedure. To demonstrate the effectiveness of the proposed model, a TSFNN based on the gradient descent algorithm (GDA) is used for comparison. Experimental results clearly show that the proposed modeling method can accurately describe the hysteresis nonlinearity of the MSMA-based actuator and has significance for its future application.

The exchange bias is of technological significance in magnetic recording and spintronic devices. Pursuing a large bias field is a long-term goal for the research field of magnetic shape memory alloys. In this work, a large bias field of 0.53 T is achieved in the Ni50Mn34In16− x Fe x ( x = 1, 3, 5) system by tuning the magnetic ground state (determined by the composition x ) and the magnetic-field history (determined by the magnetic field H FC during field cooling and the maximum field H Max during isothermal magnetization). The maximum volume fraction of the interfaces between the ferromagnetic clusters and antiferromagnetic matrix and the strong interfacial interaction are achieved by tuning the magnetic ground state and the magnetic-field history, which results in strong magnetic unidirectional anisotropy and the large exchange bias. Moreover, two guidelines were proposed to obtain the large bias field. Firstly, the composition with a magnetic ground state consisting of the dilute spin glass and the strong antiferromagnetic matrix is preferred to obtain a large bias field; secondly, tuning the magnetic-field history by enhancing H FC and reducing H Max is beneficial to achieving large exchange bias. Our work provides an effective way for designing magnetically inhomogeneous compounds with large exchange bias.

Vibration energy exists widely in nature, and the use of intelligent materials to harvest vibration energy to power microelectronic systems is a trend in the field of new energy. In this paper, the inverse effect of magnetic shape memory alloy (MSMA) that is a new intelligent material, is used to design a new kind of vibration energy harvester, which is based on integrated cantilever beam. The structure of cantilever beam and magnetic field loop are optimized, and the ideal structure model of vibration energy harvester is established. The magnetic field is analyzed by using ANSYS finite element software. On the basis of developing the prototype of the harvester, the experimental platform is built and the harvester is tested. The results show that the output voltage of the MSMA vibration energy harvester based on cantilever beam can reach more than 300 mV, which has a wide frequency band of vibration energy harvesting, and possesses a good prospect for development and application.

We report on low twinning stress of 0.2 MPa for type 1 twin boundaries with rational (101) twinning plane and 0.1 MPa for type 2 twin boundaries with rational [(1) over bar 01] twinning direction, in Ni2MnGa0.8Fe0.2 seven-layer modulated martensite exhibiting about 12% stress-induced strain. The studied samples were free of compound twins with (100) and (110) twinning planes. The martensite lattice is monoclinic and shows a long-period commensurate modulation with wave vector q=(2/7)g(110), where g(110) is the reciprocal lattice vector. The investigated alloy has high potential for practical applications due to the low twinning stress and the elevated Curie point T-C=400 K. (C) 2019 Acta Materialia Inc. Published by Elsevier Ltd.

We study Young’s modulus and damping of 10M martensite in Ni50.0Mn28.4Ga21.6 magnetic shape memory alloy using a sample without a/c twin boundaries (TBs) and maximum or zero shear stress in a/b twinning planes. Damping is ~300 times higher and modulus ~3.5 times lower when shear stress acts on a/b TBs. Ultrahigh damping and low modulus are insensitive to magnetic field, show strong strain amplitude nonlinearity and are attributed to stress-induced motion of a regular system of mobile a/b TBs. Near the reverse transformation, E001 modulus without contribution of TBs is ~10 times higher than reported previously for 10M polyvariant sample.

Here we report a systematic research on effects of Fe and Cu upon properties relevant for the magnetic shape memory effect of Ni–Mn–Ga ferromagnetic shape memory alloys. Fe and Cu were identified as elements with potential synergism to increase the martensite transformation temperature of Ni–Mn–Ga magnetic shape memory (MSM) alloys. Eighteen Ni–Mn–Ga–Fe–Cu alloys with different systematic trends in substituting the ternary elements with Cu and Fe have been investigated. We found a method to describe the effectiveness of Ni, Mn, and Cu upon raising the martensitic transformation temperature, lowering the saturation magnetization, and varying the Curie temperature. We find the martensite transformation temperature most influenced by the Ni content, followed by Mn, with a smaller effect of Cu. The saturation magnetization decreases with similar coefficients for Mn and Cu alloying. The Curie temperature monotonously decreases with Mn, but not Cu. The 10M martensite structure is stable for the composition Ni46.5Mn25+XGa25−X−YFe3.5CuY with X and Y range of 0–5.7, and 0.8–3.0. Used in combination with the total e/a, the elemental e/a-ratio gives some insight into the complex behavior of quinary MSM alloys and is a useful method of analyzing MSM alloys for improved functional properties.

Structural, elastic, electronic and magnetic properties of the Nickel-based magnetic shape memory alloys (MSMA) Ni2MnSb, Ni2MnSn and Ni2MnSb0.5Sn0.5, are investigated using the full-potential linearized plane wave plus local orbital method (FP-LAPW+lo). With Perdew-Burke-Ernzerhof (PBE) exchange-correlation, generalized gradient approximation (GGA) is used to describe the electronic exchange correlations energy. Equilibrium lattice constant, bulk modulus, and its pressure derivative are calculated and compared with available data. Using the total energy versus strain in the framework of the FP-LAPW+lo approach, we compute the elastic constants of the studied compounds in their austenite structure. Good agreement is found with other calculations both for Ni2MnSb and Ni2MnSn. Magnetic moments agree well with available results.

International audience; Thermo-mechanical treatment is an effective way to tune the microstructure and enhance the output strain of NiMn-based magnetic shape memory alloys through field driven variant reorientation or structural transformation. Comprehensive knowledge on the microstructural feature and related transformation crystallography is of great importance for the microstructure control and property optimization. In this work, we demonstrate the crossing twin of seven-layered modulated (7 M) martensite assembled in herringbone shape induced by thermo-mechanical treatment in a directionally solidified Ni50Mn30Ga20 alloy. Based on the electron backscatter diffraction (EBSD) measurements, it is found that the crossing twin is composed of four 7 M martensite variants with two mutually crossing systems of twin, i.e., type I twin and compound twin. The type I twin in the crossing twin, being with {1 –2 10}7 M as the twinning plane, is quite different from that of the self-accommodated martensite (i.e., {1 –2 –10}7 M as the twinning plane). A novel transformation orientation relationship between austenite and 7 M martensite in crossing twin is resolved to be {1 0 1}A//{1 –2 10}7 M and A//7 M, in contrast to that of self-accommodated case, i.e., {1 0 1}A//{1 –2 –10}7 M and A//7 M. By using the experimentally determined orientation relationship between two phases to construct the deformation gradient matrix, the underlying mechanism for the selection of twinning system is further discussed.

The present paper introduces a novel test procedure for the quasistatic magnetic characterization of FSMA (ferromagnetic shape memory alloy) components under mechanical loading for the use in actuator-level modelling. Its development was necessary due to certain requirements coming from the twin structure and shape of typical FSMA components which are not met by the presented test setups up to now. The measurements carried out in the developed test setup are verified by a reference sample and FE simulations. Error sources are discussed and the main systematic error is calculated. After correcting the remaining error, the acquire data correspond well to data from literature and show a physical consistency. The developed test procedure is hence able to measure effective but absolute magnetization properties of FSMA components under mechanical loading. The data directly and can be applied to any kind of actuator level modeling.

$$\hbox {Ni}_{2}\hbox {MnGa}$$ magnetic shape memory alloys have a microstructure consisting of martensite variants, and magnetic domains exist in each martensite variant. In the absence of a magnetic field, the magnetic domains are equally distributed so that the net magnetization of the material is zero. Application of a magnetic field or mechanical stress can rearrange the martensite variants and magnetic domains. This study focuses on understanding the effects that magnetic field, compressive stress and magneto-mechanical loading have on the magnetic domains, by measuring and quantifying magnetic domain volume fraction and magnetization vector rotation using direct imaging. In particular, a magneto-optical indicator film in conjunction with polarization microscopy was used to visualize the evolution of the magnetic domains and magnetization vector rotation of a $$\hbox {Ni}_{2}\hbox {MnGa}$$ sample for different load cases, namely varying magnetic field at constant strain, and varying compressive stress at a constant magnetic field. Our experiments revealed that the applied magnetic field causes change in domain volume fraction at different rates in each variant, and that domain wall motion is not always fully reversible. Magnetization vector rotation, however, was found to be reversible for all loading cases tested.

Twin boundary motion is the basic mechanism responsible for fast actuation of magnetic shape memory (MSM) alloys. Previous studies implied on a wide diversity of twin boundary velocities measured under similar conditions. Here, a data set of more than 400 velocity values is measured under conditions that are relevant for MSM applications and represents the dynamic behavior of 73 twin boundaries. Velocities are measured using an electro-mechanical setup that applies a controllable $$\upmu{\text{s}}$$ -scale force pulse and combines force measurements with high-speed imaging. The latter allows extracting velocities of individual twin boundaries, which are then correlated to the macroscopic stress in the sample. The appearance of type I twins is more prevalent than type II, resulting a much larger data set for type I twins. Statistical analysis of velocity points of type I twins reveals an increasing trend of the velocity with the macroscopic stress, as well as useful information on the probability distribution of velocity data. Velocities of type II twins exhibit large variability over a relatively narrow stress range. This can reason the large differences in maximal velocities reported previously for this twin type. The obtained statistical data can improve the design and modeling of MSM actuators.

This work investigates the effects of time dependency for isothermal sintering on additive manufactured Ni–Mn–Ga magnetic shape memory alloys. Binder jetting additive manufacturing was used to produce Ni–Mn–Ga parts from pre-alloyed powders. Additive manufacturing via the binder jetting technique produces parts with intrinsic porosities, based on the morphology of the source material. The Ni–Mn–Ga parts printed in this study using the binder jetting method possessed average densities of ~ 46% before sintering. These samples were sintered at 1353 K in increments of 10 h up to 50 h. Based on this temperature and time frame, (1) microstructural evolution, (2) crystallographic phase analysis, (3) transformation behaviors, and (4) thermal–physical properties were investigated. The additive manufactured Ni–Mn–Ga samples exhibited increases in densities, from ~ 74 to ~ 83% due to solid-state diffusion mechanisms. X-ray diffraction reveals that all of the additive manufactured samples have the 5 M martensitic phase at room temperature. Reversible martensitic transformation temperatures were recorded during heating and cooling cycles through differential scanning calorimetry, which indicate austenitic phase transformations occurring slightly above ambient temperatures. Additionally, analysis of the heating and cooling cycles prescribes that the entropy and Gibb’s energies decrease over the reversible martensitic transformations as sintering time increases. It is envisioned that this study will support a more synergistic manufacturing process between binder jetting additive manufacturing and post-heat treatment processes for Ni–Mn–Ga shape memory alloys.

In this contribution we present a constitutive modelling framework for magnetic shape memory alloys (MSMA) that builds on a global variational principle. The approach relies on concepts of energy relaxation and generalised notions of convexity to compute effective energy hulls to the non-convex energy landscape associated with the underlying multi-phase solid, from which the prediction of microstructure evolution results. In this sense it fundamentally distinguishes itself from MSMA models that essentially follow phenomenological concepts of classical plasticity (Kiefer and Lagoudas, 2005; 2009). The microstructure is not spatially resolved, but micro-scale quantities are taken into account in an effective sense by additional state variables—such as volume fractions or interface orientations—and appropriate mixture rules. The model allows all mechanisms central to MSMA behaviour—i.e. variant switching, magnetisation rotation away from easy axes, and magnetic domain evolution—to occur simultaneously. The authors have previously been able to demonstrate that such a modelling approach can quantitatively capture the key characteristics of single-crystalline MSMA response under standard loading scenarios (Kiefer et al., 2015). The modelling framework presented here is now further able to predict much more general response features, such as variant switching diagrams, magnetic field-biased pseudo-elasticity and the influence of specimen shape anisotropy. Moreover, the global variational framework is formulated in a manner that lends itself to finite element implementation. In this work, however, numerical examples are considered in which the nonlocal nature of the demagnetisation field is taken into account in an approximate sense through appropriate shape factors.

Magnetic shape memory alloy (MSMA) based actuators are extensively applied in the fields of precision manufacturing and micro/nano technology. Nevertheless, the inherent hysteresis in the MSMA-based actuator severely hinders its further application. In this letter, the characteristics of hysteresis behavior under different input signals are investigated. Then, a nonlinear auto-regressive moving average with exogenous inputs (NARMAX) model based on a diagonal recurrent neural network (DRNN) is used to construct the rate-dependent hysteresis model. To improve the capability of characterizing the multi-valued mapping of the hysteresis loop, the play operator is adopted as the exogenous variable function of the NARMAX model. To verify the effectiveness of the proposed model, a series of comparisons are implemented. The experimental results show that the proposed NARMAX model based on the DRNN exhibits excellent modeling performance.

The transformation temperatures, magnetization behavior, shape memory behavior, and mechanical properties of polycrystalline Ni45Mn40Co5Sb10-xBx(at.%) (x = 0, 1, 2, 3, 4, 5) alloys were systematically investigated. It was revealed that substituting Sb with B drastically increases the transformation temperatures, while it decreases the saturation magnetization due to the alteration of electron concentration of the matrix and formation of Co-rich second phases. With the substitution of Sb with 5% B, martensite start temperature and activation energy were increased from 50 to 316.8 degrees C, and 185 to 722.6 kJ mol(-1), respectively. The thermal cycling under stress, superelasticity, and failure experiments showed that shape memory properties and strength were improved by the substitution of Sb with B. The shape memory effect with maximum recoverable strain of 1.6% was observed with in Ni45Mn40Co5Sb9B1, and perfect superelasticity was exhibited at 220 degrees C in Ni45Mn40Co5Sb8B2. It was concluded that NiMnCoSb alloys can be used as high-temperature magnetic shape memory alloys as they exhibit transformation temperatures above 100 degrees C and show promising shape memory and superelasticity behavior, and there is a magnetization difference between their transforming phases.

The effect of excess Mn on the stability of modulation and elastic properties was investigated using ab initio electronic structure calculations in Ni–Mn–Ga magnetic shape memory alloy. We used the structure of four layered modulated martensite known as 4O to describe modulation of the martensitic lattice. We found that elastic properties of stoichiometric 4O martensite are very similar to elastic properties of 10M martensite reported in previous calculations. The modulated structure becomes less stable than nonmodulated martensite above 3 at.% of excess Mn which corresponds very well to experimental observation at low temperature. Elastic properties of NM martensite are not significantly affected by Mn content nor local arrangements of Mn-excess atoms. We also found that Mn-excess atoms prefer occupation of distant positions for low Mn-excess composition. The occupation of closest position is preferred for alloys with higher content of Mn.

This chapter summarizes the development history and research status of magnetic shape memory alloys. The crystal structures are analyzed according to the phase diagram. Finally, the basic concept and properties related to martensitic transformation or twin boundary motion are introduced, including shape memory effect, superelasticity, magnetic-field induced strain and magnetocaloric properties.

Heusler Ni-Mn-Sn-based alloys are good candidates for magnetic refrigeration. This application is based on cycling processes. In this work, thermal cycles (100) have been performed in three ribbons produced by melt-spinning to check the thermal stability and the magnetic response. After cycling, the temperatures were slowly shifted and the thermodynamic properties were reduced, the entropy changed at about 3–5%. Likewise, the thermomagnetic response remains similar. Thus, these candidates maintain enough thermal stability and magnetic response after cycling. Likewise, Cu addition shifts the structural transformation to higher temperatures, whereas the Curie temperature is always near 310 K. Regarding magnetic shape memory applications, the best candidate is the Ni49Mn36 Sn14Cu1 alloy This study was funded by University of Girona PONT2020-01 and Spanish Mineco MAT2016-75967-P projects

The synergistic control of resistance reduction and sealing poses challenges to enhancing the rapid dynamic response ability of servo hydraulic cylinders, the key to solving this problem is effectively controlling the sealing gap value. In this study, a micro-variation between the hydraulic cylinder and the piston based on the disadvantage of conventional seals, constant gap seals, and lip gap seals was constructed, MSMA assist support blocks were designed on the piston to form a gap seal strip, then, the sealing gap value could be changed by controlling the magnetic field intensity. Simultaneously, the effects of magnetic field strength, parts-manufacturing precision, temperature, and hysteresis on the micro-variation in the MSMA were analyzed, and effective solutions were proposed. Finally, experiments on the magnetic field, temperature, and hysteresis were conducted by the measurement system. The results showed that the variable value of the sealing gap with the MSMA is feasible under ideal conditions, and can effectively change the amount of MSMA expansion by controlling the magnetic field strength, temperature, preload, etc., and then change the amount of the sealing gap of the hydraulic cylinder. This is the key to achieving friction and sealing control, which plays a crucial and active role in improving the efficiency of hydraulic systems. However, the impact of hysteresis effects cannot be ignored, which will be the main problem to be solved in the future.

In this paper, a low-frequency vibration energy harvester based on magnetic shape memory alloys (MSMAs) is proposed to harvest the vibration energy. The principle of energy harvesting using the magnetic shape memory alloy is clarified, and the related experimental schematic diagram is designed. When the harvester is vibrated, the cantilever beam will exert force on the sample, which will make the martensite reorientation causing the axial magnetic polarization to change and leads to the change of magnetic flux. Therefore, when a pick-up coil is surrounded by the specimen, voltage will be induced according to Faraday's law. The magnetic field generated by the NdFeB magnet in the experimental device is simulated and verified, and the modal analysis of the cantilever beam is implemented to ensure that it can meet the requirements. Then the energy harvesting experiment is carried out and the induced voltage generated at low frequency (no more than 50 Hz) is depicted. The RMS values of the induced voltage at different frequencies are calculated. At low frequencies, the experimental results show that the proposed energy harvester has advantages in generating voltage compared with other devices, which further demonstrates the effectiveness of using magnetic shape memory alloy to capture low-frequency vibration energy and can provide references for the acoustic energy harvesting to some extent.

Ni-Mn-Ga alloys, a kind of magnetic shape memory alloys (MSMAs), can exhibit maximum expansion strains of 6% when an external magnetic field applied, and have a fast response time, high power density, which making MSMAbased actuators kHz capable. For this reason, we presented a kind of low-frequency, small-sized longitudinal transducer driven by Ni-Mn-Ga in this paper and fabricated a prototype. The finite element method was used to design and analyze the magnetic induction intensity distribution in the drive magnetic circuit. Meanwhile, the displacement of the radiating surface in the air and the sound source level in the water of the transducer were measured. According to the results, the radiating surface displacement of the transducer can reach up to 0.12 mm in the air, and the sound source level in the water exceeded 130 dB. The strain test result of the Ni-Mn-Ga transducer is much higher than that of piezoelectric ceramics or Terfenol-D with the same dimensions. Therefore, it can be realized by using Ni-Mn-Ga alloys to design a low-frequency transducer with a small size.

We investigate the cross coupling between parallel operating thermo-magnetic generators (TMGs) on their dynamic performance and power output. TMGs are an emerging technology for waste heat recovery. Here, TMG operation relies on the abrupt drop of magnetization at the Curie temperature of a magnetic shape memory (MSMA) film of Ni-Mn-Ga mounted at the front of a cantilever and on rapid heat transfer due to the film's large surface-to-volume ratio. Parallel designs are highly demanded to increase power output. When exposed to heat source temperatures Ts of 110-170 °C, resonant self-oscillation of each cantilever is excited in the range of 50-70 Hz resulting in a power output up to $30\ \text{mW}/\text{cm}^{3}$ for each TMG. At low Ts, oscillations remain stable even for a small distance $D$ of 0.4 mm between cantilevers, while at $\text{Ts}\ \geq\ 150^{\circ}\mathrm{C}$ , instabilities occur below $D=1$ mm affecting power output.

The phase stability, martensitic transition and magnetism of Zn-doped Heusler alloys Mn2NiGa1-xZnx (x = 0, 0.25, 0.5, 0.75, 1) were investigated by first-principles calculations. In Mn2NiGa1-xZnx, Zn atom plays a similar role like main-group element Ga and also occupies the D site. A possible reason for this is the closed 3d-shell of Zn. The austenite-martensite energy difference ΔEM in Mn2NiGa1-xZnx increases rapidly with the doping of Zn, suggesting that the martensitic transformation temperature can be elevated with only a little Zn doping in Mn2NiGa. This can be meaningful for the development of new magnetic shape memory alloys. The variation of ΔEM can be explained by comparing the DOS structure of the austenite and martensite: The Jahn-Teller instability of Mn2NiGa1-xZnx austenitic phase is enhanced with increasing Zn content. An increase of the c/a ratio is also observed at the same time. Zn-doping does not change the magnetic structure of Mn2NiGa1-xZnx, they are always ferrimagnets within the range studied. The magnetic properties of these alloys are mainly characterized by the antiparallel coupled Mn spin moments.

Polycrystalline Ni50Mn25Ga20Gd5 (at%) magnetic shape memory alloy was investigated in the as-prepared state and after annealing at 1430 K for 3 h. Microstructural analysis reveals dual-phase nature of the material with substantial distinction between Gd-rich and Gd-poor phases. Magnetic measurements performed in wide range of temperatures confirm reversible martensitic transformation in the annealed sample undergoing close to the room temperature. When it comes to the magnetic transition, the Curie temperature of the investigated alloy remains approximately unchanged at 370 K. Topography investigations conducted on the atomic force microscope in contact mode allow to measure 8 mm difference between minimum and maximum point of the martensite profile. The results from a series of nanoindentation tests show that hardness of the Gd-rich phase is 23%–35% higher than hardness of the Gd-poor phase, depending on the annealing state.

The magnetic field-induced stress and strain of magnetic shape memory alloy (MSMA) are fundamental to describe its magnetomechanical behavior. In order to investigate the operating characteristics of MSMA-based actuator, this paper presents a 3-D quasi-static modeling approach of magnetomechanical behavior of MSMA with the improved constitutive equation by introducing the activation field strength. The relationships between three critical parameters of the activation field strength, the maximum of strain, as well as the saturation field strength, and the pre-compressing force are obtained by fitting the data collected from the experiment. Two kinds of test specimen in different geometric dimensions are studied by the numerical modeling method. Considering that the key material parameters vary dramatically depending on the size and composition, verifications through experiments show that this numerical modeling and simulation can accurately describe the force and deformation characteristics of MSMA. The modeling analysis and simulation results are significant to design of the actuator based on MSMA to predict the actuator performance under the given working conditions.