In this study, we introduce a novel material descriptor and corresponding mechanical criteria to guide the development of low-fatigue shape memory alloys. Our approach synergistically combines compatibility theories, crystallographic algorithms, and micromechanical experiments to optimize materials through a two-parameter compositional tuning strategy. We demonstrate this method on a series of CuAlx1Mnx2alloys, where the atomic composition vectorx=(x1,x2)is an element of[0.17,0.22]x[0.09,0.11]. By employing a scalar-valued function to index the functional fatigue property based on cofactor conditions, we analyze the continuity and extremes with respect to compositional variables. Through just three iterative development steps, we identify the composition CuAl20.2Mn11.3, achievinga reduction in thermal hysteresis by a factor of 2 and enhancing mechanical reversibility upto 1000 cycles. This result underscores the potential of mathematical methods in designingcomplex materials with desirable mechanical properties. Ourfindings not only provide atheoretical framework for the design of shape memory alloys but also highlight the impor-tance of integrating theoretical and experimental techniques to achieve optimal materialproperties

Shape memory alloys that can deform and then spring back to their original shape, have found a wide range of applications in the medical field, from heart valves to stents. As we push the boundaries of technology creating smaller, more precise tools for delicate surgery treatments, the behavior of these alloys at tiny scales becomes increasingly crucial. In this study, we discover that the size effect of critical stress required for stress-induced phase transformation is not universal. We propose an orientation-dependent power decay law, indicating a specific increase in critical stress for pillars smaller than 1 micrometer for the nominally soft [001] and hard [111] orientations. Additionally, we observe high transformability with 11% recoverable strain under high stress (2 GPa) through lattice frustration at 200 nm scale. This research opens new avenues for exploring the superior elastic behavior of shape memory alloys for nanodevices.

Superelastic alloys used for stents, biomedical implants, and solid-state cooling devices rely on their reversible stress -induced martensitic transformations. These applications require the alloy to sustain high deformability over millions of cycles without failure. Here, we report an alloy capable of enduring 10 x 107 tensile stress -induced phase transformations while still exhibiting over 2% recoverable elastic strains. After millions of cycles, the alloy is highly reversible with zero stress hysteresis. We show that the major martensite variant is reversible even after multimillions of cycles under tensile loadings with a highly coherent (11 over bar 0)A interface. This discovery provides new insights into martensitic transformation, and may guide the development of superelastic alloys for multimillion cycling applications.

Ferroelectric materials are widely used in energy applications due to their field-driven multiferroic properties. The stress-induced phase transformation plays an important role in the functionality over repeated and consecutive operation cycles, especially at the micro/nanoscales. Here we report a systematic in-situ uniaxial compression tests on cuboidal Barium titanate (BaTiO3) 3 ) nanopillars with size varying from 100 nm to 3000 nm, by which we explore the stress-induced transformation and its interplay with plastic deformation. We confirm the superelasticity achieved in pillars by martensitic phase transformation from tetragonal to orthorhombic. There exists a critical size, 330 nm, for the yield stress. Above 330 nm, martensitic phase transformation aids slip along the plane with a low Schmid factor, in turn, the pseudo-compatible twins form within the shear band. The scaling exponent of size-dependent yield strength is found to be exactly 1. For nanopillars smaller than 330 nm, no twins form, only slips with large Schmid factors are activated, and size effect vanishes. All pillars with sizes from 100 nm to 300 nm achieve the theoretical yield limit around 9 GPa. Our experimental results uncover the interplay between twins and slips in BaTiO3 3 nanopillars, which pave the way for the optimization of microstructure design of ferroelectric materials for microelectronic applications at small scales.

The in situ micromechanical tensile tests are conducted to characterize the superelastic behaviors for [223], [1214], [325] and [205] oriented Cu67Al24Mn9 micro-slats. The stress-induced martensitic transformations are captured in all textures corresponding to strong crystallographic anisotropy. We propose a one-dimensional constitutive model considering the directional anisotropy of elastic modulus for cubic symmetry and the crystallographic compatibility of twinned martensite. The modeled mechanical behaviors agree with the micromechanical tensile tests well, which suggests that the formation of compatible twins is the primary deformation mechanism. Particularly in the [205] texture, we observed formation of nano-cavities (<100nm) on the lateral surface of the micro-slat. Based on the analysis of compatible martensite twin laminates and fcc slip systems, we theorize that the massive normal elongation and little lateral shear cause the formation, stretching and growth of nano-cavities at nano scales to accommodate the external loads. As a result, the structural and functional fatigue resistance is improved compared to other textures. The experimental and theoretical results in this paper are potentially useful to guide the texture design of Cu-based shape memory alloy for high transformation strain and low functional fatigue.

Shape memory alloy undergoing reversible martensitic transformation is an important class of metallic functional materials. In the past two decades, the development of shape memory alloys enables great advances in biomedical devices, microelectronics, and energy conversions. As the application scales of these devices get smaller and smaller, it is very critical to understand and tune the mechanical properties of shape memory alloys in nanoscale regime. While there are extensive reviews of shape memory alloys regarding their macroscopic properties, metallurgical treatments, and applications in the design of microdevices, their nanomechanics are not well summarized and thoroughly compared transversely among different experimental setups. This review provides an insight of the latest discoveries in nanomechanics of NiTi-based and Cu-based shape memory alloys, which sorts out the size effects, the deformation mechanisms, and the functional fatigue of the miniaturized samples in single-crystalline and polycrystalline formats.

Pyroelectric energy converter is a functional capacitor using pyroelectric material as the dielectric layer. Utilizing the first-order phase transformation of the material, the pyroelectric device can generate adequate electricity within small temperature fluctuations. However, most pyroelectric capacitors are leaking during energy conversion. In this paper, we analyze the thermodynamics of pyroelectric energy conversion with consideration of the electric leakage. Our thermodynamic model is verified by experiments using three phase-transforming ferroelectric materials with different pyroelectric properties and leakage behaviors. We demonstrate that the impact of leakage for electric generation is prominent, and sometimes may be confused with the actual power generation by pyroelectricity. We discover an ideal material candidate, (Ba,Ca)(Ti,Zr,Ce)O$_3$, which exhibits large pyroelectric current and extremely low leakage current. The pyroelectric converter made of this material generates 1.95 $\mu$A/cm$^2$ pyroelectric current density and 0.2 J/cm$^3$ pyroelectric work density even after 1389 thermodynamic conversion cycles.

We propose a new experimental mechanics method: dual beam-shear differential interference microscopy (DInM) for full-field surface deformation measurement. The method integrates the principles of differential interference contrast, photoelasticity, digital image correlation and the theories of continuum mechanics for a 4D quantification of the surface topography. Our first DInM prototype provides the lateral resolution of 787nm for up to 12% measurable out-of-plane strains. The resolution can be improved by using the shorter spectrum light and higher magnification objective lens. We use our system to characterize the buckling profile of Si microribbon on an elastomer substrate, which was verified by atomic force microscopy. We also demonstrate the stress-induced phase transformation in NiTi alloy by our system. The evolution of the surface topographies and the full-field deformation gradients are successfully captured and quantified. The dynamic measurement provides the information to calculate the relative transformation strains between phases of different symmetries. The establishment of dual beam-shear DInM opens a new avenue in the field of experimental meso/micromechanics.

Both crystallographic compatibility and grain engineering are super critical to the functionality of shape memory alloys, especially at micro- and nanoscales. Here, we report a bicrystal CuAl24Mn9 micropillar engraved at a high-angle grain boundary (GB) that exhibits enhanced reversibility under very demanding driving stress (about 600 MPa) over 10 000 transformation cycles despite its lattice parameters are far from satisfying any crystallographic compatibility conditions. We propose a new compatibility criterion regarding the GB for textured shape memory alloys, which suggests that the formation of GB compatible twin laminates in neighboring textured grains activates an interlock mechanism, which prevents dislocations from slipping across GB.

A mathematical description of crystal structure is proposed consisting of two parts: the underlying translational periodicity and the distinct atomic positions up to the symmetry operations in the unit cell, consistent with the International Tables for Crystallography. By the Cauchy-Born hypothesis, such a description can be integrated with the theory of continuum mechanics to calculate a derived crystal structure produced by solid-solid phase transformation. In addition, the expressions for the orientation relationship between the parent lattice and the derived lattice are generalized. The derived structure rationalizes the lattice parameters and the general equivalent atomic positions that assist the indexing process of X-ray diffraction analysis for low-symmetry martensitic materials undergoing phase transformation. The analysis is demonstrated in a CuAlMn shape memory alloy. From its austenite phase (L21 face-centered cubic structure), it is identified that the derived martensitic structure has orthorhombic symmetry Pmmn with the derived lattice parameters ad = 4.36491, bd = 5.40865 and cd = 4.2402 Å, by which the complicated X-ray Laue diffraction pattern can be well indexed, and the orientation relationship can be verified.

A novel data-driven approach is proposed for analyzing synchrotron Laue X-ray microdiffraction scans based on machine learning algorithms. The basic architecture and major components of the method are formulated mathematically. It is demonstrated through typical examples including polycrystalline BaTiO3, multiphase transforming alloys and finely twinned martensite. The computational pipeline is implemented for beamline 12.3.2 at the Advanced Light Source, Lawrence Berkeley National Laboratory. The conventional analytical pathway for X-ray diffraction scans is based on a slow pattern-by-pattern crystal indexing process. This work provides a new way for analyzing X-ray diffraction 2D patterns, independent of the indexing process, and motivates further studies of X-ray diffraction patterns from the machine learning perspective for the development of suitable feature extraction, clustering and labeling algorithms.