Uni-axial compression on [001] CaFe 2 As 2 micropillars

To test the hypothesis that these materials exhibit superior superelastic properties and even can be used as shape memory compounds, we investigated the mechanical response of a solution-grown, single crystal of CaFe 2 As 2 using an in situ microcompression test in a scanning electron microscope (SEM) and in situ cryogenic neutron scattering test under pressure. We grew, out of a Sn rich quaternary melt, a millimeter-sized plate-like single crystal that possesses mirror-like (001) and {103} facets (Fig. 1b). Both hydrostatic pressure and thermal expansion studies suggest that the phase transformation occurs mainly due to a structural collapse along c axis of the tetragonal (or orthorhombic) lattice17. Thus, uni-axial compression tests along c axis would be the most straightforward way to characterize either superelastic, actuation, or potential shape memory properties. Due to the plate-like geometry and small dimensions of solution-grown single crystals, it is difficult to perform conventional, bulk-scale, uni-axial mechanical tests. In addition, the irregular shapes of these as-grown crystals would result in a non-uniform stress state during loading, which could lead to un-intended plastic deformation or fracture during mechanical testing. To mitigate these issues with conventional testing, we utilize the recently developed microcompression technique that uses a focused-ion beam to create cylindrical micropillars and a flat-end nanoindenter to compress the single crystal precisely along its c axis18,19,20. Micropillars with 2 μm diameters were fabricated on the (001) surface of the single crystal, so that our micropillars are aligned along the c-axis of tetragonal lattice (Fig. 1c). Then, uni-axial compression tests were performed in SEM.

First, we compressed a single micropillar up to ~ 11.3% strain three times, and the stress–strain curves demonstrate recoverable and repeatable responses for each cycle (Fig. 2a). The SEM images before and after three cycles of compression revealed no difference in height (the inset of Fig. 2a). Thus, this large amount of deformation is fully recovered. Also, the repeatable nature of the stress–strain response implies that there is no residual damage or evidence of a stochastic transformation. This behavior is similar with that of NiTiHf shape memory alloys that exhibit an excellent repeatability with a negligible amount of fatigue damage21. We also performed cyclic tests with ~ 10% strain and 100 cycles, and confirmed that this large deformation is fully recoverable and repeatable even after 100 cycles (Supplementary Fig. 1 and Supplementary Note 1). Note that the shape of micropillar in the inset of Fig. 2a is obscured due to the ring around a micropillar. At the final stage of focused-ion beam milling, we use a thin co-centric circular pattern that, when is sometimes insufficiently wide, leaves a ring of material behind. Because the focused-ion beam is highly uniform over the pattern, however, the shape of micropillar is nearly symmetric, and the ring is not attached to a micropillar. We used the height of the right side of the micropillar, which is clearly visible, and also further confirmed that the stress–strain curves in Fig. 2a overlaps the stress–strain curve in Fig. 2c, which was measured from the symmetric micropillar in Fig. 1c (before compression) and the inset of Fig. 2c (after compression). Also, we always carefully inspect the measured displacement from in situ deformation movies. Thus, all stress–strain data in this manuscript were correctly measured (Supplementary Fig. 2 and Supplementary Note 2). Additional stress–strain curves are also available in Supplementary Fig. 3, which confirm that our method produces reasonably consistent superelasticity results.

Fig. 2 Demonstration of superelasticity including large recoverable strains and high yield strengths. a A three stress–strain curves of same [001]-oriented CaFe 2 As 2 micropillar; the inset shows no height change even after three cycles of 11.3 % strain compression. Remarkably, the stress–strain curves appear identical, indicating that there is no residual damage accumulation during cyclic deformation, which is typically observed in shape memory alloys or ceramics especially at small length scales7, 11. Stress–strain data of Ni-Ti alloy also was included for comparison. Two snapshots of in situ compression show the significant compressive elastic deformation, which cannot be achieved in other metallic or intermetallic materials; scale bar, 1 μm. b Electron density distributions at ambient pressure and under c-axis compression; the formation of As–As bonding, which is indicated by arrows, induces the structural collapse and the 10% height reduction. The iso-surface level used was 0.035 and the max is 0.1 (red). c Experimental and computational (DFT) stress–strain curves of [001]-oriented CaFe 2 As 2 micropillar up to the yield point. We intentionally terminated the stress–strain data of DFT simulation at the experimental yield strength because the remaining data above the yield strength is not meaningful in the current analysis. The inset shows the plastic slip in the \([30\bar 1](103)\) slip system Full size image

The stress–strain curves exhibit three distinct deformation behaviors (stage I, II, and III) (Fig. 2a). Note that the existence of non-linear behavior (stage II) resembles that of typical SMMs, which corresponds to a phase transformation7, 11. Another feature that is notable in the stress–strain curves is the relative narrowness of the hysteresis loop, which is also quantitatively different from standard SMMs that exhibit substantially larger hysteresis loops at room temperature. Thus, CaFe 2 As 2 would be able to release the large amount of work without significant damping effects. Most crystalline SMMs exhibit a non-linear response through the martensitic–austenitic phase transformation. Because this shear transformation almost always produces a localized shear strain on the micrometer scale, a kinked shape is easily observed during compression on a single crystalline micropillar of conventional shape memory materials11. For CaFe 2 As 2 , however, we confirmed via our in situ mechanical test of various micropillars observed along different viewpoints and at a high magnification (up to 7000×) that CaFe 2 As 2 always shows only a height reduction along the c axis (loading direction) without any lateral motion of the pillar, the formation of slip steps, or strain bursts. These results imply that phase transformation is not related to a shear process at all (Fig. 2a) (Supplementary Movie 1) but rather a simple reduction in lattice constant along c axis that is expected for this compound undergoing a cT phase transition. Thus, superelasticity in CaFe 2 As 2 is exhibited by non-martensitic–austenitic phase transformation. In our experiment, shear-like phenomena are only observed in conjunction with plastic yielding (see the formation of shear slip steps in the inset of Fig. 2c). Also, we confirmed that as long as the micropillar diameter is large enough to neglect the FIB effect damage layer (typically, pillar diameter >1 µm), CaFe 2 As 2 micropillars exhibit no size dependence in stress–strain curve. This would be because the unit length scale of the phase transition is only the dimension of the unit cell, which is far smaller than the micropillar diameter.

Density functional theory calculations on superelasticity

In order to provide additional insight into the unusual form of superelasticity in CaFe 2 As 2 , we performed the density functional theory (DFT) simulations of the compression process. Since DFT calculations are done at 0 K, the stable phase of CaFe 2 As 2 predicted is the anti-ferromagnetic orthorhombic phase, which is different from the paramagnetic tetragonal phase of our room temperature experiments22. As revealed previous work on the phase transformation in CaFe 2 As 2 , the formation of As–As bonds has been identified as the primary process to responsible for the structural collapse regardless of initial structure (tetragonal or orthorhombic)22. Thus, it is still possible to capture the essential physics of how the formation of As–As bonds affects stress–strain curves and the stability of the cT phase at a low temperature. This information will be critical for understanding of unusual shape memory effects at an ultracold temperature later. Our DFT simulations of a single unit cell, Supplementary Fig. 4 show that initially the CaFe 2 As 2 crystal undergoes elastic deformation in stage I and collapses into the cT phase in stage II, as a consequence of new bonding formation between As-As layers and the loss of all magnetism12. An electron density distribution map, (Fig. 2b), shows the electron density overlap of As-As bonding under uni-axial compression. At this moment, bonding–antibonding splitting of As 4p z orbitals is increased and this is an important indication that a bond formation has taken place23. The stress–strain curve of unit cell (Supplementary Fig. 4) shows the sudden decrease in stress, which indicates the sudden change (phase transformation) in structure and properties. The strong attraction force between As–As layers collapses the lattice structure. However, the simulations of a single unit cell miss the gradual phase transformation expected in the real material. To simulate this realistic case, we use a composite model that minimizes the total enthalpy under load control, similar to the experiments, to determine the phase fractions of the orthorhombic and cT phases via minimization (Supplementary Figs. 5, 6, 7 and Supplementary Note 3). The resulting stress–strain curve is shown in Fig. 2c. DFT simulations, in conjunction with a simple analytical model, demonstrate that in the course of compression, the partial phase transformation is energetically more favorable than the full/abrupt transformation of the entire volume of specimen. Thus, the volume fraction of cT phase gradually increases in the course of deformation, leading to continuous stress–strain curve in Fig. 2c. The unit cell still undergoes the abrupt structural collapse locally, but the macroscopic response of micropillar exhibits the gradual and continuous deformation. Note that the transtion to the cT phase is not associated with an invariant plane as is common in traditional shape memory materials, which is an un-distorted and un-rotated plane, in the strictest sense. This is because there is a small in-plane strain on the (001) plane during the phase transition (Fig. 2b). However, this strain is small making this plane the most favorable interface between the two phases. The details of microstructural evolution could be confirmed by by performing in situ electron back-scattered diffraction (EBSD) or in situ transmission electron microscope (TEM) micropillar compression test.

Despite the large number of assumptions in our model, it clearly captures all phases of deformation including the smooth stage II transition from orthorhombic to cT phase. Indeed, the formation of As–As bonding (phase transformation) is the major process that induces the non-linearity of stress–strain curve. Note that superelasticity mechanism in CaFe 2 As 2 is unique because it is not exhibited by the martensite-austenite phase transformation of conventional shape memory alloys and ceramics. From these single unit cell and composite simulations, it is clear that the large values of recoverable strain observed in CaFe 2 As 2 occur by the combination of linear elastic strain, hyperelastic strain, and phase transformation strain.

Superelasticity and actuation performances

It is clear from our experiments that we have yet to observe the maximum recoverable strain, the yield strength, the maximum work release per unit volume, and the actuation work per unit volume of this material. To determine these values in compression, we performed an additional micropillar compression test, increasing stress until we see either plastic deformation or fracture, and determined that the elastic limit is ~ 13.4 % and the yield stress is ~ 3.7 GPa, both of which is even higher than those of single crystalline shape memory ceramic micropillars, which have been known to possess the current state-of-the-art superelastic work and actuation work per unit volume (Figs. 2c and 3). Returning to the composite material model we see that at the experimentally determined yield stress, the simulation suggests ~ 13% recoverable strain, which agrees well with our experimental results. Intermetallic compounds typically possess strong directional atomic bonds, which explain why the strength is much higher than shape memory alloys or even shape memory ceramics. In fact, the strong directional bonds help suppress plastic deformation in CaFe 2 As 2 , increasing the recoverable strain from roughly ~ 7% associated with the phase change to ~13.4% which includes elastic strain.

Fig. 3 A comparison of CaFe 2 As 2 with other structural and actuator materials. Actuator stress and strain for various actuator materials and systems. Contours of constant specific work are indicated by dashed lines (adapted from Lai et al.11, Huber et al.26 and Lang et al.27). Both experimental and DFT data are included. All four experimental data came from stress–strain curves in Supplementary Fig. 3c. Note that CaFe 2 As 2 exhibit actuation capapbility comparable to shape memory ceramic micropillars Full size image

The combination of the high recoverable strains (13.4%) and high yield strengths (3.7 GPa) are even higher than those of shape memory ceramic micropillars11. Also, low hysteresis area allows CaFe 2 As 2 to absorb and release ultra-high work per unit volume with minimal dissipation at room temperature. The stress–strain curves in Fig. 2a suggest that the energy loss by damping is about 10% based on the ratio of the areas under the loading-to-unloading curves. Assuming that this percent loss is similar up to elastic limit, we can estimate the maximum possible work absorption/release per unit volume by using 90% of the area under the stress–strain curves beween zero strain and the elastic limit in Fig. 2c: this corresponds to 1.76 × 108 J/m3 (experiment) and 1.57 × 108 J/m3 (DFT) for the absorption of, and 1.58 × 108 J/m3 (experiment) and 1.40 × 108 J/m3 (DFT) for the release of work per unit volume (for 10% of damping effect). These results imply that CaFe 2 As 2 is able to release the superelastic work about 10~ 1000 times larger than most engineering materials (e.g., stainless steel24: 105 J/m3, Zr-based bulk metallic glass25: 2 × 107 J/m3, shape memory ceramic micropillars11: 4 × 107 J/m3: shape memory alloys11: 105 J/m3). Some shape memory metallic alloys could show the larger recoverable strain. Due to their low yield strength and high damping effect, however, their work release per unit volume (~105 J/m3) is much lower than CaFe 2 As 2 (1.76 × 108 J/m3). Furthermore, as noted before, the actuation capability is determined by the maximum possible actuation work per unit volume which is the area below a stress–strain curve within phase transformation strain range (the gray trapezoidal area in Fig. 2c), which corresponds to ~ 5.15 × 107 J/m3. This can be estimated by multiplying the actuation strain by the average actuation stress (\(\sigma _{PT}^{ave}\)), which is the average of the onset (\(\sigma _{PT}^{onset}\)) and offset (\(\sigma _{PT}^{offset}\)) phase transformation stresses (Fig. 2c). On the basis of this scheme, we can compare the actuation capability of CaFe 2 As 2 with other actuation systems by locating our four micropillar results and one DFT result with the actuation stress and the average actuation stress (Supplementary Fig. 8, Supplementary Table 1, and Supplementary Note 4). Fig. 3 shows a comparison of actuation capability, by plotting actuation stress vs. actuation strain, of CaFe 2 As 2 compared with other materials11, 26, 27. Note that materials with higher actuation work per unit volume appear toward the top and right of the plot in Fig. 3. Conventional shape memory alloys, such as bulk Ni-Ti alloy, exhibit much lower actuation work per unit volume, as also evidenced by their low actuation stress (see the gray colored stress–strain curve in Fig. 2a). As a special case, Norfleet et al.28 investigated shape memory properties of Ni–Ti micropillars. Size effects can improve the phase transformation stress of Ni–Ti alloys, up to 800 MPa. Also, the transformation strain of Ni–Ti micropillar is around 0.06. Then, actuation work per unit volume of Ni–Ti micropillar (800 MPa × 0.06 = 4.8 × 107 J/m3) is similar with that of CaFe 2 As 2 (~ 5.15 × 107 J/m3). Figure 3 clearly shows that CaFe 2 As 2 shows the comparable actuation work per unit volume with shape memory ceramic micropillars (the current state-of-the-art) or the high-end of shape memory alloy. Thus, CaFe 2 As 2 exhibit excellent actuation work per unit volume, compared to shape memory alloys.

Cryogenic linear shape memory behavior

The narrow hysteresis loop of CaFe 2 As 2 would be associated with the different stress required to form and break the As–As bonds. This leads to the existence of hysteresis in stress–strain curve of CaFe 2 As 2 . Our DFT simulation results (Supplementary Fig. 4) and neutron scattering results by Goldman et al.22 (Fig. 4a) show that CaFe 2 As 2 exhibits the maximum width of hysteresis at 0 K. Without thermal vibrations, the As–As bonds are not broken even after the complete removal of compression stress. The neutron scattering experiment (Fig. 4a) show that a hydrostatic tensile load of 0.25 GPa (or −0.25 GPa pressure) is required to destabilize cT phase at 0 K22. As the temperature increases, thermal vibrations help the destabilization of the As–As bonds under some amount of compression stress (or pressure), leading to the narrower hysteresis. Figure 4a shows clearly that the width of hysteresis area becomes narrower as the temperature increases. Thus, increasing a temperature would be an effective way to make the hysteresis loop narrower and to maximize the release of mechanical work. Vice versa, it is possible to expect the cryogenic shape memory effects due to the metastability of cT phase at 0 K.

Fig. 4 Linear shape memory effect and thermal actuation in cryogenic environments. a The temperature-pressure phase diagram for CaFe 2 As 2 22, neutron scattering data of b (004) O plane of orthorhombic phase at T = 50 K with increasing pressure, c (004) cT plane of collapsed tetragonal phase at T = 50 K with increasing pressure, d (004) cT plane of collapsed tetragonal phase at T = 50 K with decreasing pressure, e (004) O plane of orthorhombic phase at T = 50 K and p = 50 MPa, f (004) cT plane of collapsed tetragonal phase at p = 300 MPa with increasing temperature, g (004) planes of tetragonal and collapsed tetragonal phases at p = 470 MPa with increasing and decreasing temperature. Schematic diagrams of h one way linear shape memory effect and i thermal actuation Full size image

The DFT simulation of a single unit cell predicts that the cT phase is metastable after loading-unloading cycle at 0 K (Supplementary Fig. 4). In other words, cT phase is not transformed into orthorhombic phase even though the applied stress is completely removed at 0 K. However, our experimental data shows the full strain recovery at room temperature, suggesting that the cT phase is unstable at room temperature but may well be metastable near 0 K at atmospheric pressure. Metastability of cT phase is a pre-requisite to exhibit shape memory behavior. Thus, this work includes important evidence that, taken together with our current superelasticity results, suggests the existence of a cryogenic linear shape memory effect. On the basis of this evidence, it is possible to suggest, two different deformation routes, path 1-2-3-4 and path 1′-2′, to demonstrate the cryogenic linear shape memory effects and thermal actuation, respectively (Fig. 4). In order to prove the existence of cryogenic shape memory effects, we conducted in situ cryogenic neutron scattering measurement on a single crystal of CaFe 2 As 2 using a He gas pressure cell in a displex cryogenic refrigerator22. In this experiment, it is possible to control both temperature and pressure and to check the occurrence of phase transformation at the same time (Fig. 4a). First, the temperature was decreased down to 50 K, and neutron scattering data clearly shows that the phase becomes orthorhombic (path 1 and Fig. 4b). Then, the pressure was increased until cT transition occurs (path 2 and Fig. 4b, c), and we confirmed that cT transition occurs between 350 and 400 MPa. A pre-requisite of the shape memory effect is metastability of the deformed state. To achieve this metastability of cT phase, we decreased the pressure down to 300 MPa (path 3), and neutron scattering data confirms that the transition to the T phase does not occur even below the critical pressure for the forward transition (350–400 MPa) (Fig. 4d). The transition to the O phase (at 50 K) only occurs when the pressure is decreased below 50 MPa (Fig. 4e). This clearly confirms that cT phase is metastable after path 3 and satisfies the pre-requisite of shape memory effect, which is metastable deformed state. After preparing the sample in the cT phase, within the hysteresis region, the temperature was increased from 50 to 100 K to destabilize the cT phase, and the transition to the orthorhombic phase occurs (path 4 in Fig. 4a, f). This is truly shape memory effect that exhibits the shape recovery by making the metastable deformed state unstable by applying the stimulus, heat (Fig. 4h). The transformation strain along a and b axes are much smaller than the transformation strain along c axis. Thus, the cT transition is nearly linear volume transformation (the volume changes only by the lattice expansion/contraction along c axis). Thus, cryogenic linear shape memory effects do exist in CaFe 2 As 2 . On the basis of the phase diagram (Fig. 4a), the cryogenic linear shape memory effects can be shown at the pressure between 0 and 400 MPa and at the temperature between 0 and 110 K. Thus, theoretically, it is possible to achieve shape memory effects near 0 K, and this property would be useful to develop a cryogenic linear actuator working even in deep space (3 K). In addition, path 1′ and 2′ also shows the thermal actuation at a temperature higher than 100 K by the phase transformation between tetragonal and cT phase. Neutron scattering data clearly shows that this transformation occurs and thermal actuation is available (Fig. 4g) as shown in schematic diagram (Fig. 4i).