Introduction

Shape memory alloys (SMAs) undergo a reversible, diffusionless, solid-state phase transformation between martensitic and austenitic crystal structures in response to external stimuli (temperature, stress, electric field, magnetic field, or combinations thereof), accompanied by strains ranging up to and beyond 10%. The ability of returning to its original shape upon heating was defined as shape memory effect (SME) [1, 2]. At least two crystal structures are involved, i.e., austenite and martensite. Austenite is stable at high temperature (T > AF, austenite finish temperature) and transforms to twinned martensite upon cooling (T < MS, martensite start temperature). Upon loading, twinned martensite converts to detwinned martensite, with strain generated and remaining after unloading. Detwinned martensite transforms to austenite by heating, with the shape recovered. This cycle is called one-way SME. The shape can also be remembered in both states, when the material shows the two-way SME or reversible SME. In addition, a reversible transformation between austenite and martensite at T > AF, by applying mechanical load is called superelasticity (SE).

During the past decades, SMAs have been extensively investigated in terms of fundamental mechanism and engineering applications, for instance the most commercial SMAs, NiTi alloys, show excellent SME and mechanical properties [3, 4]. SMAs have been used in numerous fields, such as microelectromechanical systems (MEMS) [5, 6], medicine [7, 8], automotive [9], and aerospace [10]. However, conventional SMAs can suffer from oxidation and instability, especially in nanoscale [11, 12], e.g., Ti content in NiTi unavoidably leads to changes in surface and interfacial layers due to oxidation, thereby reducing transforming performance [13].

SMEs are also observed in some oxides, so-called shape memory oxides (SMOs). Two types are mainly of interest in research: martensitic shape memory ceramics and ferroelectric shape memory ceramics [2]. Compared to SMAs, SMOs have high strength, high-temperature operation and chemical resistance, which could fulfill some application needs that SMAs can’t [1, 14, 15]. Details on the fundamental mechanism of different types of SMOs can be found in review articles [2, 14, 16], which therefore will not be focused in this review. The drawbacks of SMOs are that the magnitude of recoverable strain is relatively low and micro-cracking can appear during transformation cycling. For example, cracking was observed in polycrystalline ZrO2 (zirconia) after about 5 cycles transformation cycles, in which about ~ 2% of strain was achieved [17]. The transformation mismatch stress developed during the phase transformation, especially between neighboring grains of different orientations, leads to the formation of micro-cracks and fracture most often along grain boundaries. Latest studies on the small-scaling of SMOs pave a way for overcoming issues with brittleness and thus facilitating practical applications of SMOs. Some SMOs at the micro/nanoscales are capable to exhibit profound SE and SME [18, 19].

This review mainly summarizes the recent progress in the research of the mechanical performance of SMOs at small scales. First, the concept and application of small-scaling in SMA is presented. Second, three SMO material systems, based on zirconia (ZrO2), bismuth ferrite (BiFeO3), and vanadium dioxide (VO2), on which micro/nanoscale methodology have been proven to be effective, are presented.

Concepts and Characteristics of SMAs and SMOs at Small Scales

The exploration of small-scaling effects on SME/SE started on SMAs, e.g., for the application of these alloys in miniaturized functional devices such as MEMS. Studies on NiTi-based SMA, the most extensively researched SMA material system, show that the martensitic transformation of SMA and the accompanying SME and SE properties are strongly affected by the grain size at the nanoscale. In the case that the grain size d is much finer than the sample size D, the parent austenite phase is completely stabilized once d is smaller than a critical value, typically in the range of several tens of nanometers. The martensitic transformation is therefore suppressed [12]. For example, Waitz et al. [20] reported that the transformation of nanocrystalline NiTi SMAs to martensite is no longer observed once d reaches a critical size. In study of the size dependence of the martensitic transformation in SMAs, a model was proposed with respect to the transformation thermodynamics in nanocrystalline NiTi [20]. The following relations applies during the transformation: ΔGA−M = Eb, with ΔGA−M = GA − GM being the chemical free energy difference per unit volume between the austenite GA and martensite GM, and Eb = Es + Ei + Ef being the energy barrier per unit of transformed volume which includes the increase in the total elastic strain energy Es, interface energy Ei associated with the formation of martensite in austenite matrix and total irreversible frictional energy Ef of the transformation. By calculation, it was concluded that the Eb of the transformation to martensite increases with decreasing grain size. As a result, the martensitic phase transformation is suppressed when the grain size is < 100 nm and completely suppressed at a critical size of 50 nm.

In contrast, when d is comparable to D, nanoscale SMAs can show excellent properties. For example, Juan et al. [21] performed nanocompression test on pillars of various size made from single-crystal Cu–Al–Ni alloys, and found that both austenite and martensite are more stable in nanoscale pillars than they are in bulk. The stress–strain curve (Fig. 1b) during the martensitic transformation exhibits a large hysteresis area in the closed loading–unloading loop, which suggests a very high figure of merit for mechanical damping. This size effect makes Cu–Al–Ni nano/micro-structures attractive for damping applications in nano- and microscale devices. Further, Cu–Al–Ni small-scale pillars show a strong size effect on the critical stress that induces the martensitic transformation, in which a power-law size dependence is observed for the nanoscale SE [22]. It is noteworthy that the concept of small-scale pillar is not applicable to NiTi SMA: similar compression test on sub-micropillars shows a loss of PE for samples with diameter < 200 nm, although in situ TEM observations confirm the occurrence of martensitic transformation [23, 24]. It was proposed that the loss of PE is related to a suppression of strain recovery, which might be due to a Ga+ ion damage layer from FIB fabrication of the pillar [25].

Fig. 1
figure 1

a SEM image of a submicrometer pillar milled by FIB on a Cu–Al–Ni [001] oriented single crystal. b Comparison of the compression behavior in bulk single crystals Cu–Al–Ni (black curves) at 363 and 305 K, and submicrometer pillar at 295 K. “Reprinted from Reference [21] with permission, Copyright (2009), Springer Nature.” c Stress–strain curves of polycrystalline Cu–14.1Al–4.2Ni and oligocrystalline Cu–13.7Al–5Ni. The schematics in the top right corner of each graph show the grain structure of each sample. “Reprinted from Reference [27] with permission, Copyright (2012), John Wiley and Sons”

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Oligocrystalline shape memory alloys (oSMAs) [26,27,28] are investigated as they show a greater total surface area than total grain boundary area. Because of less transformation strain at grain boundaries and triple junctions, oSMAs can achieve single crystal-like SMAs properties without failure or fracture. For example, Cu–Al–Ni oSMAs wires show recoverable strain up to ~ 7%. In comparison, bulk SMAs normally fracture at very small strain (Fig. 1c). oSMAs structures show increase in cycle life of up to two orders of magnitude over polycrystals. Size effects in both the transformation stresses and temperature of Cu–Al–Ni oSMAs were observed, and an increase in the hysteresis area in the stress–strain loop in oSMAs with smaller size was also observed, which suggests the application for energy damping.

In summary two methods are used to improve the shape memory performance of SMAs. One method is to reduce the size of the sample, because a smaller sample leads to a higher surface-to-volume ratio and lattice dilation and mismatch stresses from the transformation can be relaxed at free surface. The other method is to reduce the number of grains in the sample, e.g., to use an oligocrystal or single crystal, which can reduce the stress mismatch and transformation constraint occurring at the grain boundary area. As mentioned above in the thermodynamic equation, energy barrier Es is attributed to the elastic mismatch stresses induced by the phase transformation, when the dilatation of the transformed region is accommodated by the surrounding austenite matrix. When it comes to the microscale pillar or oSMAs, Es is largely reduced because the mismatch stress can be relaxed at larger free surface region. Meanwhile, transformation constraint from the grain boundaries is also reduced. As a result, the microscale pillar and oSMAs can show excellent SMEs [21, 27].

SMEs of thin film SMA were also researched, showing interesting properties and giving more insights into its nanoscale application. For example, a study on B2–B19 martensitic transformation in Ti51Ni38Cu11 thin film with thickness ranging from 750 to 50 nm shows that AF and MS temperatures decreased with decreasing film thickness but increased again for film thickness < 100 nm [29]. The 75 nm thick film showed zero hysteresis and an AF well above room temperature, which make it promising for nanoscale application. Although it was mentioned that the transformation of NiTi is suppressed for very small grain sizes, substrate-attached Ti51Ni38Cu11 thin films as thin as 50 nm still exhibit phase transformation. Studies on SMA thin films also suggest that the effect of the surface reaction layer should be considered when nanoscale shape memory thin films are used. For instance, the reaction layers formed on the surface of Ti51Ni38Cu11 thin film significantly change the chemical composition of the transforming phase [13]. As a result, the phase transformation properties are influenced by film thickness, because the deviation from the nominal chemical composition is larger for thinner films. For example, for a 50 nm thin film, the Ti content was reduced by 9 at.%, whereas the Ni content was increased by 5 at.%. The Cu content stays relatively constant for films of different thickness. To investigate the scaling effects in SMA thin films, some micromachined test platforms such as microfabricated devices and thin film microbridges were designed [30]. Those devices allow for nanomechanical tests and enable electrical characterization before, during, and after the performance of these tests. Furthermore, in situ TEM nanomanipulation on freestanding thin film microbridges is possible with the device.

ZrO2

Low Recoverable Strain of SME in Polycrystalline/Bulk ZrO2

ZrO2 has three polymorphs: monoclinic (m), tetragonal (t) and cubic (c), among which, the t-m martensitic transformation is of interest because of the accompanying SME [31,32,33,34]. Volume expansion of 4–5% and shear strain of 14–15% occur during the phase transformation [35]. For pure ZrO2, the transformation t \(\to\) m occurs at ~ 950 °C, whereas the reverse transformation m \(\to\) t occurs at ~ 1170 °C. By modifying zirconia with other oxides, for example, ceria and yttria, the transformation temperatures (TT) can be tuned and t-ZrO2 can be stabilized at room temperature [17, 36].

The SME of ZrO2 was first observed in magnesia-partially-stabilized-zirconia (MgO-PSZ) ceramics [37]: a bent MgO-PSZ bar recovered its shape upon heating above 800 °C. The reversible deformation strain is only 0.5%, limited by the brittleness of the bulk ceramic. The precipitates of t-ZrO2 in the c-ZrO2 matrix undergo the martensitic transformation. Morel et al. reported PE and SME in CeO2-stabilized tetragonal zirconia polycrystals (Ce-TZP) containing 12 mol% CeO2 [17]. The as-sintered ceramics were entirely t-ZrO2 with grain sizes of ~ 1–2.8 μm. Upon loading at room temperature, a plastic deformation up to 1% occurs due to the t \(\to\) m phase transformation. The strain remains after the load is removed. Subsequent heating above 186 °C results in the recovery of approximately 95% strain because of the reverse m \(\to\) t phase transformation. Zhang et al. studied the SME of ZrO2 samples with different contents of CeO2 (8–12 mol%) and Y2O3 (0.25–0.75 mol%) and found that the 8Ce–0.50Y–TZP shows a recoverable strain of ~ 1.2% and no micro-cracks were found after shape recovery [38]. As mentioned, ZrO2 SMO can be used for applications where SMA is not applicable, such as high-temperature devices in oxidative environment. However, its practical application is limited by the relatively low recoverable strain and tendency of micro-cracking.

SME of ZrO2 at Small Scales

Methods that have been used in SMAs research (Sect. 2) were considered to be used to explore and achieve higher strains without micro-cracks in ZrO2 ceramics during the phase transformation [27, 28, 39]. Different forms of ZrO2 in small scale have been proven to show excellent SME, i.e., submicrometer pillars [18], micro-particles [40], granular packing [41], foam [42], as summarized in Fig. 2. The aim of small-scaling is to reduce the mismatch stress at grain boundaries and increase the surface area to relax the stress during the martensitic transformation.

Fig. 2
figure 2

SE/SME manifested in different forms of small-scale ZrO2 SMO: a Micro-compression stress–strain curve for 16 mol% CeO2–ZrO2 pillar with effective diameter deff = 1.82 μm, in which the initial elastic loading of austenite is followed by forward transformation plateaus during the formation of martensite. Reversion to austenite is observed during unloading. “Reprinted from Reference [18] with permission, Copyright (2013), The American Association for the Advancement of Science.” b Load–displacement curves of 14 mol% CeO2–ZrO2 particles. Inset SEM images show the particle before and after compression and after heating. “Reprinted from Reference [40] with permission, Copyright (2017), John Wiley and Sons.” c Load–displacement curves of 300 mg (ZrO2)0.85-(CeO2)0.15 powders (tetragonal phase) under cyclic loading from 35 to 880 MPa. “Reprinted from Reference [41] with permission, Copyright (2017), Elsevier.” d Curves of 6 mol% Ce–zirconia foam where transformation temperatures are in line with dimensional changes. “Reprinted from Reference [42] with permission, Copyright (2017), Elsevier”

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The concept was first tried on micrometer-scale pillars fabricated from polycrystalline Ce-/Y-ZrO2 by Lai et al. using focused ion-beam (FIB) milling [18]. Each micropillar can be viewed as a single crystal or oligocrystal as the size of the micropillar is designed to be smaller than or close to the average grain size of the ceramic. In the stress–strain curve of a 16 mol% CeO2–ZrO2 loaded in compression (Fig. 2a), the austenite phase first undergoes a linear elastic deformation with loading. At a critical stress, the phase transformation to the martensite phase is induced, indicated by plateaus and reduced slope in the curve. The transformation shows a large strain of 7% and was reversed upon unloading. The reversion of the transformation remains after dozens of cycles. SME was also observed from the micropillar accompanied with a large recoverable strain of 8%. A load in bending mode was applied to a pillar of 8 mol% CeO2–0.5 mol% Y2O3-ZrO2. Upon loading, the austenite pillar undergoes stress-induced transformation and forms a new shape in the martensite phase, which remains after unloading. By heating the bent pillar above AF, the transformation is reverted, and the shape of the pillar is recovered.

Further investigations on the size dependence of recoverable strain of fine-scale pillars indicates the advantage of the oligocrystalline structure with less grains, grain boundaries and triple junctions [43]. Micropillars with diameters ranging from 0.7 to 3.0 μm were fabricated by FIB from 8 mol% CeO2–0.5 mol% Y2O3–ZrO2 with average grain size of 1.7 μm. When the pillar diameter is smaller than the average grain size of the ceramic, the pillar shows significant strains from 3 to 8% during the phase transformation, without fracture. In contrast, larger pillars with diameters above 2 μm tend to fracture and show smaller strains.

As the martensitic transformation of zirconia between tetragonal and monoclinic phases is highly anisotropic, the transformation stress and strain are dependent on the crystallographic orientation. Study on the stress-induced martensitic transformation of ZrO2 macro-pillar suggests that the critical stress at which transformation occurs is orientation-dependent (Fig. 3) [44]. Not only phase transformation but also fracture and slip were observed during the compression test. For instance, the orientations near [001] and [100] require large stress for transformation and as a result fracture occurs before the transformation is triggered. While for orientation near [110], the crystal slip is favored and observed upon loading. Therefore, in practical application of SMOs, the control of orientation or texture is very important to obtain desired SME or SE performance.

Fig. 3
figure 3

a Crystal orientations of pillars on a tetragonal standard stereographic triangle, with typical load–displacement curves and corresponding the as-deformed pillar morphology for pillars that b slipped, c transformed and d fractured. “Reprinted from Reference [44] with permission, Copyright (2016), Elsevier”

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The SME of zirconia micro-particles was also studied [40]. Spherical Ce-ZrO2 with diameters in the range of 0.8–3.0 μm were synthesized by sol–gel method. The Ce–ZrO2 single-crystal particles showed excellent SME and SE properties with recoverable strain up to 4.7% (Fig. 2b). The shape memory particle containing 16 mol% ceria exhibited highly reproducible SE through over 500 load cycles.

The unveiled excellent SME and SE of ZrO2 in small-scale structures enables the development of, e.g., actuators with high work density, high energy damping and high-temperature range. For instance, work density of the SMO is determined on the order of 100 MJ/m3, which is higher than that of SMA and hydraulics. The large hysteresis area of the stress–strain loop of the small-scale ZrO2 provides a merit index of damped energy on the level of ~ 2 GPa1/2, which is two times larger as that of Cu–Al–Ni microscale SMA.

Among small-scale forms, granular packing and foam are promising for bulk applications. The SME of granular packed Ce–ZrO2 was studied by Yu et al. [41], in which particles of 3 μm or smaller were compacted and compressed. The particles were obtained by fine grinding from particles with grain size ranging up to 10 μm, which can be considered as single- or oligocrystalline. A reversible martensitic transformation was triggered by uniaxial compression, during which a remarkably high energy dissipation of ~ 2 J/g was obtained. Compared to the martensitic transformation of micropillars, the volume fraction of granular packed materials which go through the stress-induced transformation is limited to 25–40%, due to non-uniform stress distribution in powder compaction. However, aggregation of the granular SMO packing provides a possible method toward bulk-level application, such as energy dissipation and damping. Another form of small-scale SMO toward bulk application is foam SMO [42], in which micro-pores and -struts are capable to exhibit SME due to the fine scale. An open-cell foam of Ce-ZrO2 exhibited recoverable strain of ~ 2% through multiple cycles, which is higher than that of its polycrystalline bulk counterpart.

Recently, nanofiber-based yarns and springs made from 8CeO2–0.5Y2O3–ZrO2 were fabricated by electrospinning, which show a recoverable strain of up to 5% with short recovery time of 0.16 s at temperature of 328–388 °C [45]. The output stress, work density of the yarns and springs exhibited during the shape memory actuation are 14.5–22.6 MPa and 15–20 kJ/m3, which are higher than those of human muscles and some polymer-based artificial muscles. Given the high actuation temperature and chemical resistance of SMO, nanofiber-based yarns and springs are excellent candidate for artificial muscle used in extreme environment.

Other forms of ZrO2, e.g., thin films, which have not been reported yet, could also be of research interest, since it is in principle possible to have single-crystalline or oligocrystalline structures, which could lead to better SME/SE than bulk materials.

In general, the excellent SME/SE performances mentioned above are related to the small-scaling at the level of up to a few microns, based on the approach of eliminating grain boundaries. A recent study by Crystal et al. [46] takes a step further by extending the strategy to mm-scale bulk size, in which mm-scale zirconia single crystals withstand cyclic martensitic transformation through 125 cycles without obvious degradation of the strain amplitude of ~ 3% and cracking. In comparison, the strain of a large zirconia polycrystal sample during the cyclic martensitic transformation is reduced to 1.5% after 10 cycles, and a large specimen mass loss of 35% was observed after 45 cycles due to the cracking. Those results confirm that controlling the grain boundaries in the SMO will significantly affect its SME/PE performance, not only at microscale but also at mm-scale.

SME in Ferroelectrics

Due to the existence of crystalline structures of different symmetry such as cubic, tetragonal and rhombohedral in perovskite ferroelectric oxides, the SME can also be observed, which is associated with paraelectric (PE)-ferroelectric (FE) and antiferroelectric (AFE)-FE phase transformations. Upon applying electric field, the reorientation of polar domains occurs during the phase transformation.

Compared to the SME of SMAs, the recoverable strain of ferroelectrics is much lower, in general < 1%. However, driven by electric field, the response speed of the ferroelectrics is much faster, which makes shape memory ferroelectrics interesting for applications. Numerous investigations have been carried out [16, 47,48,49,50,51,52,53,54,55,56,57,58,59,60]. For example, in the system Pb0.99Nb0.02[(Zr0.6Sn0.4)1−yTiy]0.98O3 (PNZST), the SME is observed through the transformation between high-temperature AFE and low-temperature FE [16]. (Pb,La)(Zr,Sn,Ti)O3 (PLZST) tetragonal antiferroelectric single crystals show a large electric field-induced strain up to 0.76% at 110 °C [55].

Due to the toxicity of Pb, investigation on Pb-free ferroelectric systems has drawn interest. Aged BaTiO3 was reported to exhibit an electro-induced nonlinear strain of 0.75% at a field of 200 V/mm (Fig. 4), which is 40 times higher than the piezoelectric response in Pb(Zr, Ti)O3 (PZT) ceramics and more than 10 times higher than the strain in Pb(Zn1/3Nb2/3)O3–PbTiO3 (PZN-PT) single crystals at the same field [50]. The large strain is attributed to reversible domain switching and the restoring force was proposed to be a general symmetry-conforming property of point defects.

Fig. 4
figure 4

Large recoverable electric field-induced strain in an aged BaTiO3 single crystal along the [001] pseudo-cubic direction, in comparison with the piezoelectric effect of soft PZT ceramics and PZN-PT single crystals (dash lines). Inset is the set-up for displacement measurement, which used an optical displacement sensor (non-contact) to measure the strain from the free upper electrode in order to exclude the possible constraint/clamping effect. “Reprinted from Reference [50] with permission, Copyright (2004), Springer Nature”

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The multiferroic material BFO is of great interest because its properties include ferroelectricity and ferromagnetism [61, 62]. Bulk BFO has a low-symmetry rhombohedral structure with space group R3c. By strain-engineering, tetragonal variant of BFO was fabricated, and thermal-/electrical-induced martensitic-like transformation of BFO from rhombohedral (R) phase to tetragonal (T) phase was observed. The recoverable strain during the transformation is up to 14%, which is significantly larger than that exhibited by its bulk ceramic counterpart of 0.36% associated with domain switching [19, 58]. This discovery suggests the importance of strain-engineering and small scale in achieving high-performance electromechanical response in ferroelectric materials. In the following section, details about the investigations on nanoscale BFO are summarized.

SME of Nanoscale BFO

Although the ground state of BFO is the rhombohedral structure (R), it was reported that BFO thin films can be stabilized in a tetragonal phase (T) by epitaxial strain [63]. Epitaxially grown on single-crystal substrates of (001) LaAlO3 (LAO) and (110) YAlO3 (YAO) using molecular beam epitaxy, BFO films of different phases can be obtained due to varied strain levels at the interface induced by lattice mismatch. At high-strain level (high compressive strain on YAO), T phase was stabilized. In contrast, for the film grown on LAO (less compressive strain), R phase emerges as the film becomes thicker and the strain is relaxed, which leads to an outcome of T/R phase mixture on a nano level.

Figure 5a shows the phase diagram of a BFO thin film with respect to temperature and strain [63], illustrating the strain-driven morphotropic phase boundary (MPB) in BFO. MPB refers to phase transitions between tetragonal and the rhombohedral ferroelectric phases with respect to varied composition or mechanical pressure. In perovskite-type ferroelectrics, excellent electromechanical performance is usually shown in the vicinity of MPB [48, 64,65,66,67]. Similarly, T/R nanoscale phase mixture in BFO turns out to show excellent electromechanical response. By applying electric field or mechanical force, reversible transformation between T/R mixture phase and pure T or R phase has been achieved [68]. The accompanying reversible strain of ~ 5% is higher than that of traditional ferroelectric materials. Those results suggest that the MPB of BFO could also be affected by the electric field and stress that are applied to the material, in addition to the composition and the misfit strain of the material. Moreover, it was inferred that phase transformation directly between T and R phase, if possible, has the potential for larger strain.

Fig. 5
figure 5

SME in nanoscale BFO. a Calculated phase diagram of BFO as a function of temperature and misfit strain. Different phases are labeled in the diagram, in which (0,0,0) on the top denotes the cubic paraelectric phase. “Reprinted from Reference [63] with permission, Copyright (2009), The American Association for the Advancement of Science.” b–d TEM images to confirm the variation of the BFO phase from a mixed phase to pure R phase with reduced clamping, in which, b shows a cross-sectional HAADF-STEM images from a wedge-shaped lamella. Inset is the film top view to show the wedge shape. c, d are high-resolution TEM images of the film from pure R and mixed phase area. e Reversible strain from the transformation between R and T phases during temperature cycling. The sample for the test is from pure R phase area in (b). f–h The transformation is studied by first- principles calculations, and the evolutions of energy as a function of c/a ratio are presented under different conditions: f 5.8% strain, g 4% strain, h a homogeneous electric field of 0.2 V/nm along [001] direction. “Reprinted from Reference [19] with permission, Copyright (2013), Springer Nature”

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A large recoverable strain of ~ 14% for nanoscale BFO was reported by Zhang et al. [19]. In their study, pure R phase BFO was obtained from the as-deposited T/R phase mixture grown on LAO by reducing the clamping of the film from the substrate, which was achieved by reducing the lateral size of the film using FIB milling. It has been estimated that the clamping starts to decrease for lateral dimensions around 10 μm and is mostly removed around 1 μm. The T phase proportion in the T/R phase mixture decreases with lateral size until it completely disappears, which was indicated by the change of the surface topography. Direct identification of the stabilized phase in the film with less constraint was performed by TEM (Fig. 5), in which a thin cross-sectional sample with wedge shape area with thickness varying from 300 to 50 nm confirmed the structural change from R/T mixed phase to a pure R phase with substrate clamping removed.

Upon heating, pure R phase BFO starts to transform to T phase at 573 K and the phase transformation was completed at 673 K. Temperature cycling exhibited an average recoverable strain of ~ 12 ± 2%. In addition, large reversible SME in the unconstrained structure can also be driven by electric field of 1–2 MV/cm at room temperature. Moreover, the phase stability and transformation of BFO with respect to strain and electric field are interpreted by first-principles calculations. Calculated energy of BFO as a function of c/a ratio was studied at different stress and electric field conditions (Fig. 5). Under a strain of − 5.8%, there are two energy minima corresponding to the stable R and T phases, which suggested the coexistence of the phases. At smaller compressive strain, the R phase is energetically favorable, which reflected the transformation from T phase to R phase in the milled film. In the presence of electric field, the T phase showed much lower energy, which is in favor of the electric-induced phase transformation. It is noteworthy that T phase has a significantly higher energy than R phase under a strain-relaxed state, which makes the transition from R to T phase very difficult. Therefore, presence of suitable clamping stress in the BFO thin film seems to be important for the phase transformation to occur.

In summary, the large SME behavior of BFO in nanoscale originates from the structural phase transformation, which is driven by the interplay between stress, electrical field and temperature. Given the high Young’s Modulus of the material, the SME of BFO could provide a volumetric work density of 600 J/cm3, which is of great potential for applications in nanosystems.

VO2

VO2 undergoes a metal–insulator transition (MIT) at a critical temperature Tc of 68 °C, accompanied by crystalline structure change from rutile (R) to monoclinic (M) phase. Rutile VO2 (R) belongs to the crystallographic group P42/mnm, with a = b = 0.455 nm, c = 0.285 nm, in which a V atom is surrounded by an octahedron of O atoms. Along the cR axis, V atoms are equally positioned with a distance of 0.288 nm. The monoclinic VO2 (M1) phase belongs to the crystallographic group P21/c, with a = 0.575 nm, b = 0.452 nm, c = 0.538 nm, β = 122.6°. V atoms pair along the rutile c axis in zigzag type, with alternative distances of 0.312 nm and 0.265 nm [69].

Along the transformation from M phase to R phase, the unit cell of VO2 expands by ~ 0.32% (one unit cell of M phase consists of two unit cells of R phase) and the area for (011) M and (110) R planes is decreased by 1.7%, resulting in a strain of up to 1% along the rutile c axis. Because of high Young’s modulus E of VO2 (~ 140 GPa), high volume work density, given by E*ε2/2, is expected associated with the phase transition, which could be used for micro-/nanoactuators [70]. Apart from the M1 to R phase transformation, it was reported that another monoclinic phase of VO2 (M2) shows higher strain (~ − 1.7%) across its transformation into R phase [71]. M2-based actuators tend to exhibit a higher work density. M2 is a metastable phase of VO2, which can be stabilized by either applying stress along cR [72] or adding trivalent ions such as Fe3+, Cr3+ and Al3+ [73,74,75]. In addition, the electrical and optical properties of VO2 change during the phase transition, which makes VO2 interesting as a multifunctional material. In this section, we review research on the mechanical response of VO2 as well as studies on the stress change of VO2-based thin film materials libraries.

Mechanical Response of VO2

The mechanical response of VO2 is mainly studied in the form of thin films, since the thin film is able to withstand the volume change during the phase transformation cycling without fracture. For instance, a VO2-coated microcantilever was fabricated and studied by Rúa et al. [70], where 240 nm thick VO2 film was deposited by pulsed laser deposition (PLD) on Si microcantilever with dimensions of 130 μm long, 35 μm wide and 1 μm thick. The deflection of the cantilever was recorded by CCD camera at different temperatures (Fig. 6a) and a curvature change of over 2000 m−1 was observed at the temperature range where phase transition of VO2 occurs, which results in recoverable stress of ~ 1 GPa. It is noteworthy that strain of VO2 in the microcantilever is about 0.3%, smaller than theoretical value, which is limited by the polycrystalline characteristic of VO2 used in the study. With randomly oriented grains, the strain from cR-oriented grains is compensated to some extent by that from aR- and bR-oriented grains because of the opposite directions of those strains.

Fig. 6
figure 6

SMEs in VO2-based cantilevers: a deflection of a single VO2-coated Si cantilever. “Reprinted from Reference [70] with permission, Copyright (2010), AIP Publishing.” b A balm-structure microactuator made of Cr/VO2 bimorphs. The actuator can open and close at different temperature because of the curvature change during the phase transformation. “Reprinted from Reference [80] with permission, Copyright (2012), American Chemical Society”

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In contrast, a microcantilever made of single-crystal VO2 exhibits colossal thermal–mechanical actuation [76]. Single-crystal VO2 microbeams grown along cR axis were coated with Cr to form bilayer cantilevers. The curvature change of the cantilever is about 4000/m K as the phase transformation occurs, which is 10 times higher that of the polycrystalline VO2/Si cantilevers. The work density of single-crystal VO2 is theoretically 7 J/cm3, using E of 140 GPa and strain of 1%, which is comparable to that of SMAs and more than one order of magnitude higher than that of electrostrictive polymer. Moreover, a study was performed on V0.976Cr0.024O2-coated (VO2 M2) cantilevers to investigate the phase transformation from R to M2. It was reported that the VO2 M2-coated cantilever shows larger curvature change of 2900 m−1, in comparison to 1850 m−1 for a VO2-coated cantilever [77].

Researches on VO2-based actuators have also been carried out. For instance, electro-thermally driven VO2-based actuators were studied, which consist of SiO2, Ti/Pt metal electrode/heater layers and a VO2 active layer [78, 79]. The top Pt layer serves as an integrated heater for the actuator. The VO2 layer of 200 nm thickness was fabricated by PLD. The final thickness of the cantilever is about 1 μm. By Joule heating, total deflections of 68.7 and 28.5 μm were observed for 300 and 200 μm long cantilevers, respectively. It was found that the current needed for maximum deflection is dependent on the ambient conditions, and power needed for triggering the phase transition of VO2 is significantly smaller when operated in vacuum than in air. The cut-off frequency (f3dB) of the 300 μm long actuator operated in vacuum is 29 Hz, whereas it is 541 Hz when operated in air because of strong convection heat losses.

Similar VO2-based actuators were also fabricated and studied by Liu et al. [80]. Cr/VO2 bimorph actuators were fabricated with the thickness of VO2 in the nanoscale ranging from 100 to 300 nm. Figure 6b shows the optical images of bending Cr/VO2 cantilevers at two temperatures across phase transition. It was observed that the Cr/VO2 bimorph actuators exhibit high displacement-to-length ratio, which is one important performance of microscale actuation. A palm structure made of many Cr/VO2 bimorph cantilevers works as a thermally driven microactuator. By varying temperature from room temperature to 80 °C, the palm can repeatedly open and close, which might be used to capturing and releasing objects at microlevel. The actuators show work density over 0.63 J/cm3 at frequencies up to 6 kHz in both ambient and aqueous conditions.

Transition Properties Tuning in V–M (Metal)–O Libraries

The advantages such as the superior performance and microscale manufacturability make the VO2-based actuator promising applications in microelectromechanical systems [80]. An even more beneficial aspect of such an actuator is that its performance could be flexibly modified by tuning the phase transformation properties of the active layer VO2. For example, Tc can be influenced by the addition of third elements to VO2: e.g., it is increased by addition of Cr [77], Ti [81], whereas it is decreased by W [82] and Mo [83]. It is likely that the mechanical response of VO2 across the IMT is also influenced, considering structural distortions induced by the addition of a third element. Transition properties tuning, including Tc and stress change of V–M–O were studied by combinatorial depositions and high-throughput characterizations.

In V–W–O libraries [84], it was observed that when W content x in V1−xWxO2 increases from 0.007 to 0.044 the crystalline structure gradually shifts from the VO2 (M) phase to the VO2 (R) phase. Meanwhile, Tc was decreased by 15 K/at.% W, accompanied with a wider transition range and a narrower hysteresis with a minimal value of 1.8 K. To study the mechanical response of V1−xWxO2, a library was deposited on a Si3N4/SiO2-coated Si cantilever array wafer. The temperature-dependent stress change σ (T) of films with different W content through the phase transition was measured (Fig. 7a). Compared with σ (T) of ~ 700 MPa of a VO2 film, σ (T) in V1−xWxO2 films decreases to ~ 250 MPa. Meanwhile, σ (T) becomes less abrupt and occurs over a wider temperature range with decreased transition temperatures.

Fig. 7
figure 7

The temperature-dependent stress change of a V–W–O libraries with different W contents. The stress change was normalized to the stress at 100 °C. “Reprinted from Reference [84] with permission, Copyright (2018), American Chemical Society.” b V–Cr–O libraries with different Cr contents. “Reprinted from Reference [85] with permission, Copyright (2020), American Chemical Society”

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In V–Cr–O libraries [85], gradual changes in the crystalline structures of VO2 were observed in the thin film libraries at room temperature as the M1 phase exists for Cr < 1.2 at.%, the M2 phase for Cr > 4.2 at.% and an intermediate T phase in between. Tc was increased by 4.9 K/at.% in the composition range 2.8 at.% < Cr < 7.3 at.% and 1.2 K/at.% for Cr > 7.3 at.%. V–Cr–O libraries were deposited on stress sensor to study their stress change. High-throughput stress (σ(T)) measurements (Fig. 7b) indicate that the addition of Cr increased the stress change across the phase transformation up to 1.3 GPa for a Cr content of 3.3 at.%. It was found that the mechanical performance of V–Cr–O is also affected by fraction of other oxide and crystallographic orientation. As a result, the stress change of V–Cr–O library decreased to 380 MPa with Cr contents increased from 3.3 at.% to 9 at.%.

Summary and Outlook

Comparisons between SMAs and SMOs are presented in Table 1 and Fig. 8. SMOs at small scale show excellent mechanical response during the phase transformation: Ce-ZrO2 micropillars show large strain of up to 7% upon compression loading, nanoscale BiFeO3 thin films with clamping removed can achieve a maximum strain of up to 14%, VO2 single-crystal actuator of small scale has the potential of providing high work density comparable to SMAs. Compared to the SMAs, ZrO2 and BFO at small scale are capable to exhibit even higher work density as actuator.

Table 1 Summary of the shape memory effects of different materials
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Fig. 8
figure 8

Young’s modulus and actuation strain for various actuator materials and systems. Contours of constant specific work density are indicated by dashed lines. Data for high-strain piezoelectric ceramics, magnetostrictive materials, SMAs are summarized from elsewhere [86]. The performances of the small-scale SMOs are marked as dots with colors (Color figure online)

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Small-scaling provides a new path for SMOs to exhibit better mechanical response than that of their bulk counterparts. For ZrO2, small-scaling primarily reduces the grain boundary volume in the material and facilitates the formation of oligocrystalline/single-crystalline structure, which significantly eliminates the constraint and mismatch stress during the martensitic transformation. For BiFeO3, small-scaling associated with strain-engineering stabilizes pure phase instead of mixed phase in the vicinity of MPB. As a result, the largest strain is achieved in BFO via the phase transformation from pure T to pure R phase. For VO2, the mechanical response during the phase transformation is well exhibited in the form of thin film or thin film based microcantilever/actuators.

Small-scale SMOs could have promising prospects in many applications such as MEMS, energy damping, because of their superior mechanical performance. Meanwhile, similar methodology might be applied to other SMOs to modify their mechanical response. By small-scaling and strain-engineering, the amount of grain/domain boundaries can be reduced to relax the transformation constraint. Moreover, with tuning the phase boundaries (MPB in ferroelectrics systems) in the complex phase diagram of SMOs, for example, by varying the content of the second oxide in ZrO2 system and by changing the content of M in the V–M–O system, new transformation performance might be explored.