Structural phase transformation is a fundamental carrier of both elastic (reversible) and plastic (irreversible) strains and offers many novel physical, mechanical, and functional properties that conventional elasticity and plasticity carriers cannot offer, including giant elastic response [also called pseudo-or superelasticity (SE)] (1, 2), shape memory effect (SME) (3,4), Invar and Elinvar anomalies (5)(6)(7), piezoelectricity (8), and electro-and magnetostrictions (9,10). However, because structural phase transformations behave so differently from the intrinsic elastic carrier (change in atomic bound length and angle) and conventional plastic carriers (such as dislocations), they may have been overlooked as general elasticity/plasticity carriers and thus underappreciated in alloy design. For example, the strain release by a structural phase transformation is usually highly nonlinear, taking place in an avalanche fashion within a narrow temperature or stress range, and is difficult to control. Therefore, the main objective of the current review is to put together recent experimental and theoretical efforts devoted to regulating and utilizing structural phase transformations for controlled elastic and plastic strain release under applied external fields. Since controlled plastic strain release and enhanced work-hardening capacity by phase transformations in transformation-induced plasticity steels and Ti alloys have been reviewed recently (11)(12)(13), the current review focuses on strain glass transition and controlled pseudoelastic strain release.
A typical example of utilizing structural phase transformations as strain carriers in alloy design is the development of shape memory alloys (SMAs) that have attracted much attention because of their SME and SE (14). The SME and SE have led to many advanced applications of SMAs in robotics, automotive, aerospace, and biomedical fields (15)(16)(17). However, the structural phase transformation that underpins the SME and SE of SMAs, called martensitic transformation, is sharp, strongly first order, and shear dominant. It propagates at the velocity of sound traveling in solids and produces self-accommodating long-range ordered strain domains by autocatalysis. The individual domains are called martensitic variants (or transformation variants or deformation variants), and the long-range ordered strain domain patterns can be regarded as strain crystals, in contrast to the dynamic strain fluctuations present in austenite (strain liquid) (18) as shown schematically in Figure 1. The responses of martensitic transformations to external fields such as stress and temperature are highly nonlinear, showing large stress-strain or temperature-strain hysteresis and narrow stress or temperature range of activation. These characteristics have made them unsuitable for applications requiring high positioning accuracy, wide temperature windows, and low energy loss.
In recent years, extensive efforts have been made both experimentally and theoretically to tame martensitic transformations for controlled strain release. One way of doing so is to turn the sharp, strongly first-order martensitic transformation into a broadly smeared, apparently continuous, high order-like strain glass transition by defect engineering. The strain glass transition was first reportedinNi 50+x Ti 50-x SMAs by doping with excess Ni (x ≥ 1.5). It is characterized by the formation of mottled nanodomains of martensite (i.e., a strain glass state) through a freezing transition and exhibits a continuous transformation behavior upon loading/unloading or cooling/heating cycling (18). Strain glass describes a structural state with static (dynamically frozen) nanodomains of transformation strains (i.e., martensitic variants). These nanodomains typically have mottled or tweed morphology depending on the elastic anisotropy of the system, similar to the microstructure seen during a premartensitic transformation where the nanodomains are partially frozen. The transformation strains are the order parameters that characterize structural phase transformations dominated by shear (i.e., shape change of the crystal unit cell). Such a structural state differs from the two known states of martensitic systems: a strain crystal consisting of long-range ordered strain domains such as those internally twinned herringbone martensitic structures and a strain liquid Strain-state (i.e., strain liquid, strain crystal, and strain glass) diagram of ferroelastic systems (19). T nd , M s ,andT g represent the transition temperature of nanodomain formation, martensitic phase transformation start temperature, and strain glass transition temperature, respectively. The strain state changes from a strain liquid (the parent phase, with weak and random strain fluctuations) to a partially frozen, sticky strain liquid (a precursory strain state, with some static nanodomains of martensite) to a strain crystal (normal martensite, with long-range ordered strain domains that arrange into a self-accommodating polytwin pattern) at low defect concentrations or to a strain class (fully frozen nanodomains of martensite, with the nanodomains represented by red and blue ovals)at high defect concentrations. consisting of random and dynamic strain domains that are present in austenite (19). These three strain states and their relationships are shown in the strain-state phase diagram in Figure 1.
Strain glass belongs to the family of ferroic glasses, which also includes spin glass/cluster spin glass and relaxor ferroelectrics (ferroelectric glasses) (20,21). Although spin glass/cluster spin glass and relaxor ferroelectrics were discovered many decades ago, frozen tweed (i.e., strain glass) (22) was first shown by computer simulations in martensitic systems in the 1990s, and strain glass transition was first discovered by experimental measurements in 2005 (18). These ferroic glasses are defined by disordered states or nanodomains of their corresponding order parameters that characterize the ferroic phase transformations [i.e., strain in strain glass, spin in spin glass, and polarization in relaxor (Figure 2a)], which is different from oxide glasses or metallic glasses that have disordered atomic structures. In other words, oxide and metallic glasses are amorphous, while ferroic glasses are crystalline. The ferroic glass states are characterized by nanodomains of the order parameters (spin, electric dipole, and lattice strain) (Figure 2b) and frequency dispersion of elastic stiffness S [the inverse of elastic modulus (i.e., E -1 )], dielectric permittivity ε, and magnetic susceptibility χ ′ (Figure 2c).
Stress-carrying defects such as point defects, nanoprecipitates, and dislocations will create local lattice distortions and generate a random stress/strain field that interferes with the nucleation and growth of martensite. If such a random stress/strain field percolates in the system (23,24), it will completely suppress autocatalytic events during nucleation and growth and prevent the formation of self-accommodating long-range ordered transformation strain patterns (e.g., internally
)/ε/χ' T a Order parameter b Nanodomain c Frequency dispersion
The parallelism among the three ferroic glasses. (a) Order parameters (strain, electric dipole, and spin) characterizing the ferroic states. The strain describes the shear from a high symmetry phase (cubic lattice) to a low symmetry phase (parallelogram lattice) with the double-sided arrows representing the strain tensor. The electric dipole describes the charge displacement due to the symmetry change, with red arrows representing the electric dipole vectors. The spin ordering describes the change of magnetic interaction, with black arrows representing the spin vectors at different lattice positions. (b) Nanodomain structures of ferroic glasses. Different colored ovals represent nanodomains with different variants (i.e., different arrow directions). (c)FrequencydispersionofstiffnessS (the inverse of elastic modulus E -1 ), dielectric permittivity ε, and magnetic susceptibility χ ′ for strain glass, relaxor, and spin glass, respectively. Different colored lines represent different frequencies. twinned herringbone structures in martensite) and, thus, render a sharp martensitic transformation a smooth strain glass transition (18,(25)(26)(27)(28)(29)(30). A strain glass transition is smooth because the local stress field from random defects induces the formation of certain martensitic variants at temperatures much higher than the martensitic transformation start temperature, M s ,oratstress levels much lower than the critical stress for stress-induced martensitic transformation, σ 0 ,o f the defect-free counterpart. The growth of these martensitic domains is confined by the adjacent non-self-accommodating domains (because they are induced by the random defects, not by autocatalysis), and, thus, the transformation goes to completion at a much lower temperature or much higher stress.
Figure 1 shows a strain-state transition diagram (or phase diagram for short) in ferroelastic systems. At relatively high temperatures, the high symmetry parent phase (i.e., austenite) is stable, but strain fluctuations at nanometer scale occur dynamically in the system, and the amplitudes of the fluctuations depend on the curvature of the Landau free energy at zero strain at a given temperature. This is the strain liquid state. The martensitic phase becomes more and more stable as the temperature decreases, and the system will transform into either a long-range ordered strain domain pattern such as that seen in internally twinned herringbone martensite if the defect concentration is below a critical value or a nanodomain pattern of martensite having mottled or tweed morphology, depending on the elastic anisotropy of the system, if the defect concentration exceeds a critical value. The former is a strain crystal, while the latter is a strain glass.
Compared to a normal martensitic transformation, strain glass transition exhibits many unusual characteristics, including nearly linear SE with almost zero hysteresis upon cooling and heating (that underpins the Invar and Elinvar anomalies) and with ultralow elastic modulus upon loading and unloading, the disappearance of thermal peaks in differential scanning calorimetry (DSC), invariance of average structure from X-ray diffraction (XRD), and frequency dispersion of storage modulus from dynamic mechanical analysis (DMA) (18,25). As a glass state, strain glass and the other ferroic glasses (cluster spin glass and relaxor in ferromagnetic and ferroelectric systems, respectively) have shown similar or parallel characteristics as conventional oxide and metallic glasses: disorder state of the order parameters that characterize the ferroic states (i.e., strain, polarization, and magnetization), frequency dispersion or relaxation, continuous freezing process, and crystallization during long-term aging (31,32). However, ferroic glasses also exhibit some unusual kinetic characteristics compared to oxide and metallic glasses. For example, the strain glass transition becomes faster at lower temperatures (i.e., colder is faster) (33), which is in sharp contrast to the so-called colder-is-slower transition behavior of oxide and metallic glasses. Such a difference can be attributed to the competition between activation entropy and activation enthalpy, which unveils the change from colder is faster to colder is slower with the increase of defect concentration (33).
Since their discovery in 2005, many strain glass systems have been reported, including point defect-doped TiNi (25,26,34,35), TiNb (6), TiPd (36)(37)(38), TiAu (39), FeMnGa (40), NiCoGa (41), and NiMnIn (42), as well as SMAs with densely populated nanoscale precipitates (27,28) or that are heavily cold worked (29,30). According to the characteristics of a strain glass state and a strain glass transition mentioned above, a strain glass system can be identified by the following four pieces of experimental evidence to show (a) the existence of nano-sized martensitic domains by transmission electron microscopy (TEM) observations, (b) frequency dispersion of the storage modulus following Vogel-Fulcher relation from DMA, (c) invariance of average structure from XRD or disappearance of phase transition peak from DSC, and (d) continuous loss of ergodicity upon cooling from mechanical zero-field cooling/field cooling testing (Figure 3).
Below, we first discuss experimental characterizations of strain glass systems in Section 2, followed by theoretical analysis and computer simulations of strain glass transition in Section 3. We then present some challenges and outlooks of strain glass study in Section 4, followed by concluding remarks in Section 5.
Relaxor ferroelectrics were discovered in the 1960s, and cluster spin glass was discovered in 1972 (21), all by point defect doping. However, it was not until 2005, when the first strain glass system was reported in Ti 50-x Ni 50+x with doping of excess amounts of antisite defect of Ni (x = 1.5) (18), that the spectrum of ferroic glasses was completed (21). Since its discovery, strain glass has been reported in different ferroelastic systems by point defect doping (5, 6, 25, 26, 34-36, 38, 41, 43-46).
Sufficient point defect doping is necessary for the formation of strain glasses with relatively small transformation strains. As the point defect concentration increases, the martensitic domain size decreases, and when the point defect concentration exceeds a critical value, the microstructure of the system changes from a long-range ordered, internally twinned domain structure consisting of self-accommodating martensitic variants into mottled or tweed nanodomains of martensite (i.e., a strain glass state) depending on the elastic anisotropy of the system. Figure 3a,e shows the typical microstructures of strain crystal (normal martensite) and strain glass states where the difference between the degrees of strain order becomes evident. In TiNi-X SMAs, the strain glass transition requires different critical concentrations for different types of dopants, which could be attributed to their atomic radius differences and thus different lattice strains generated. The critical concentration of a given type of dopant for strain glass transition also depends on the elastic anisotropy of the system (47,48).
Since relaxors and spin glasses are created solely by point defect doping, early studies on strain glasses also focused on point defects. However, any stress-carrying defects at high enough densities should be able to serve the same (or even more effective) role as point defects in strain glass formation. More importantly, for martensitic systems having large transformation strains, point defects alone cannot suppress the martensitic transformation into a strain glass transition, no matter what the defect concentration is (49), and extended defects become necessary (30). For example, complex dislocation networks and substructures produced by cold rolling are found to have very strong impacts on martensitic transformations, even those having large transformation strains (50)(51)(52)(53), leading to nearly linear SE without obvious stress plateaus and large loss energy.
Densely populated coherent nanoprecipitates can also suppress martensitic transformations into strain glass transitions (27,54). However, with the increase of aging time and aging temperature, the system could change from strain glass transition to martensitic transition (28). Whether it is the concentration gradients in the matrix phase associated with the growing precipitates, coherency stress field generated by the precipitates, geometric confinement by the non-transforming precipitates, or all of the above (55,56) that created the strain glass state is still unclear. More detailed experimental characterizations in combination with computer simulations are required to figure this out.
In addition, strain glass has also been reported in Ti-24Nb-4Zr-8Sn (Ti2448 for short), where both nanoscale concentration modulations (57,58) and nanoscale shuffle domains (59) have been observed, both of which could have contributed to the formation of a strain glass state in the alloy. Similar transition behaviors to strain glass transition have also been reported in prestrained NiTi-Nb nanocomposite, where Nb nanowires are embedded in a NiTi SMA matrix (60). The prestraining produces plastic deformation in the Nb nanowire and introduces dislocations at the Nb nanowire and NiTi matrix interfaces, which harbor martensitic embryos that grow but are confined by neighboring Nb nanowires upon loading (61).
As mentioned in Section 1, strain glass and strain glass transition can be distinguished from normal martensite and martensitic transformation by their unique characteristics (Figure 3). Below, we present some detailed examples of these experimental characterization results.
Strain glass can be defined as a disordered state with mottled or tweed nanoscale martensitic domains. The detailed characterization of the distribution of strain domains in a strain glass system is the key evidence needed to understand the physical origin of strain glass transition. To characterize the microstructure, the average structure in microscale and local structure in nanoscale are discussed in the following sections.
Before the discovery of strain glass transition in SMAs, it was assumed that excess point defect doping completely suppresses martensitic transformation (62,63) because XRD measurements did not show any structural changes. For example, Ni 50+x Ti 50-x with x ≥ 1.5 and Ni 50-x Ti 50 Fe x with x ≥ 6 have been reported as nontransforming materials (14,64). However, the abnormal electrical resistivity change as a function of temperature and the diffuse scattering patterns observed in these materials have remained puzzles for a long time (65,66). Nanodomains of transformation strains have been reported in these systems, and they have recently been confirmed to be strain glass systems (18,19,25,34,67). The average structure of a strain glass shows no split of diffraction peak caused by the martensitic phase but a broad peak in XRD (Figure 3), which leads to diffuse scattering in the diffraction pattern (25). These can be attributed to the small size of the martensitic domains.
To explore the local structures of a strain glass, highresolution TEM images have shown the appearance of nanodomains of martensitic phases, which grow continuously upon cooling, as shown in Figure 4 (37). The martensitic nanodomains have irregular shapes due to the random spatial distribution of point defects and the random stress field associated with them (47,68,69). No internally twinned structures have been observed in these nanodomains. In other words, nanodomains of individual martensitic variants are the main characteristics of this strain glass state. However, recent computer simulations have shown that nanodomains of twinning martensite confined by nanoscale concentration modulations could also exhibit continuous transformation behavior and nearly linear SE (58), but direct experimental evidence remains to be seen. In most cases, the martensitic nanodomains have the same crystal structure (as shown by similar diffraction patterns) and transformation strains as those of regular martensite (25,37). For shuffle-mode regulated strain glasses, the shuffle domains set the scale of the strain domains (59). In this case, the shuffle nanodomains transform to shear nanodomains upon cooling with a continuous increase of the shear value (59). In NiTi-based SMAs, there exists a two-step martensitic transformation (i.e., B2-R-B19 ′ ). In this case, strain glasses with local R structure can be produced by doping point defects, while strain glasses with local B19 ′ structure can be produced only by severe cold rolling (30). The spatial confinements by local stress or concentration field (associated with random defects, spinodal decomposition, or precipitation) that form percolating networks (23,24) leading to the formation of these nanodomains of individual martensitic variants are discussed in Section 3. These nanodomains nucleate and grow continuously upon cooling and may transform into longrange ordered twinning martensite (i.e., strain crystal) at a critical temperature that is a function of defect concentration. This phenomenon is reported as spontaneous strain glass to martensite transition (32,70). Upon cooling, the volume fraction of a suppression field caused by defects decreases due to the increase of driving force for martensitic transformation, leading to the growth of martensitic nanodomains and the formation of normal martensites (23,31). Isothermal martensitic transformations have also been reported in strain glass systems below the strain glass transition temperature (T g ) (31,32,71,72), which is due to the slow domain wall motion caused by defect pinning.
Conventional martensitic transition is a first-order transition accompanied by the formation of coarse twin structure, narrow transition temperature range, and large thermal hysteresis. The formation of nanoscale martensitic domains in strain glass implies a different transition mechanism from conventional martensitic transition to capture the strain glass transition behavior, the dynamic characteristic, the freezing process, and the thermal effect. These are discussed in the following sections.
As a freezing process, all glass systems show relaxation behavior (73). The α relaxation, which is a general relaxation in different glass systems (including polymer glass, oxide glass, and metallic glass) (74)(75)(76), has also been observed in strain glass systems at T g (18). In fact, frequency dispersion of storage modulus, loss modulus, and internal friction upon cooling measured by DMA has been used as a key indicator of strain glass transition in materials once called nontransforming. As mentioned in Section 2.1.2, in strain glass systems, martensitic nanodomains form and grow continuously upon cooling. These nanodomains have a size distribution, and domains of different sizes could respond differently to an applied alternating stress/strain field, resulting in frequency dispersion. When all the martensitic domains could follow the frequency of the alternating external stress/strain field instantaneously, the system shows pure elastic characteristics, and no internal friction could be observed. If some martensitic domains cannot follow the frequency of the external field instantaneously, the system shows viscoelastic characteristics and exhibits internal friction. For normal martensitic transformation, the transformation occurs within a narrow temperature range with rapid growth of martensite via autocatalysis, leading to instantaneous formation of relatively large martensitic domains. These domains show almost the same lag phase responding to the external field at the same frequency, and the lag phase changes with the change of the applied frequency in DMA. Thus, no obvious frequency dispersion can be observed upon cooling, but the system shows different internal friction values at different frequencies. For strain glass transition, autocatalysis is completely suppressed by the random field of defects, and martensitic nanodomains nucleate randomly and grow continuously upon cooling. This leads to a broader size distribution of the nanodomains. Nanodomains of different sizes have different response rates and lag phases at different frequencies and temperatures. Thus, the frequency dispersion of strain glass transition exhibits different responses in different martensitic nanodomains under alternating loading. From energetics, there exist numerous energy basins and minimum energy barriers (saddle points) among them on the free energy landscape in the transformation strain space (67, 77) due to the existence of random defects. Different saddle points correspond to different activation energy barriers for the evolution of the transformation strains, leading to different response rates and times and thus different frequency dispersions observed.
This frequency dispersion can be described well by the Vogel-Fulcher equation (78), which can be used to estimate the ideal T g and activation energy. This time-dependent response suggests the possibility of isothermal transformations. Accordingly, experimental observations have shown an isothermal transition from strain glass to martensite at a critical defect concentration (31,71), which can be attributed to the competition between the driving force for martensitic transformation and the random field from defects that suppress the martensitic transformation. Upon cooling, the driving force increases and the suppression field from defects shrinks. Unlike athermal nucleation and growth by autocatalysis in conventional martensitic transition (79), the evolution of martensitic nanodomains in strain glass transition into internally twinned martensitic plates within a certain temperature range and a defect concentration range is time dependent (23). Due to the relatively faster movement of lattice shear (a diffusion-less process) compared to atomic diffusion in conventional glass, strain glass transition shows an atypical, colder-is-faster feature (33), and spontaneous strain glass to martensite transition has been reported upon cooling in strain glass systems within certain ranges of defect concentration (70,80). The increased driving force for martensitic transformation upon cooling can overcome the energy barrier for martensitic growth created by defects, and the system transforms into normal martensite. Similar spontaneous transition phenomena have been reported in relaxor ferroelectrics as well (81,82). Such a spontaneous strain glass to strain crystal (martensite) transition can occur within local regions, which offers an opportunity to design heterogeneous domain structures, including both microscale and nanoscale ferroelectric or ferroelastic domains with good comprehensive properties (83).
Nonergodicity is also an important feature of a glass transition, which is characterized by a history dependence of the order parameters (e.g., strain, polarization, and magnetization) in response to an external field. Experimentally nonergodicity is revealed by samples having two different cooling histories (zero-field cooling and field cooling) showing two different evolutions of the order parameter (strain) during a heating process under a fixed external stress (i.e., field heating), as shown in Figure 3h (84). A microscopic picture of such a disparity in the field-heating curves between the zero-field-cooled and field-cooled samples is as follows. For a zero-field-cooled sample, which is characterized by random nanodomains, upon field heating from the T << T g , the macroscopic strain value gradually increases as the size of the martensitic nanodomains gradually decreases; thus, some nanodomains could respond to the external stress by domain switching. When the temperature rises above T g , the volume fraction of the martensitic domains decreases rapidly, leading to a decrease in the response strain. Thus, the zero-field-cooling and field-heating curves show a hump (Figure 3h). The peak temperature corresponds to the freezing temperature, T g , in strain glass transition. For a field-cooled sample, it shows larger strain values at low temperatures (<T g ) because of the aligned (or textured) nanodomains by the applied field. Upon heating (>T g ), the volume fraction of martensitic nanodomains decreases continuously, leading to a continuous decrease of strain. The strain difference between the field-cooling-field-heating curves and the zero-field-coolingfield-heating curves decreases due to the decrease in the volume fraction of the martensitic nanodomains (Figure 3h). The two curves start to overlap at a critical temperature, defined as T nd ,at which the martensitic nanodomains disappear or appear upon heating or cooling.
It should be noted that a normal martensitic transformation (and many solid-state phase transformations) also shows a breaking of ergodicity at T < M s as a result of the frozen status of microscale strain domains (i.e., internally twinned martensite), but to a lesser extent, as the zerofield-cooling and field-cooling curves are essentially overlapping at T > A s (the start temperature of inverse transformation to austenite) (Figure 3d). This is different from a strain glass transition.
The strong first-order martensitic transformation shows a typical exothermic peak upon cooling and an endothermic peak upon heating because of the latent heat of transformation. The exothermic and endothermic peaks occur at different temperatures, which implies the existence of thermal hysteresis, typical for a first-order transition. Unlike normal martensitic transformations, however, the strain glass transition shows no obvious exothermic and endothermic peaks upon cooling and heating but rather shows a clear heat capacity hump without thermal hysteresis (18,25,34). This suggests that the strain glass transition is a high-order-like (higher than second order) continuous transition process. Note that such a continuous transformation could be attributed to an integral effect of many local first-order martensitic transformation events that occur at different temperatures or stresses (i.e., broadly smeared multiple first-order transitions). An exception to this could be the shuffle-mode regulated strain glass transition found in Ti2448 mentioned in Section 2 (59), in which the shuffle nanodomains transform to shear nanodomains upon cooling with a continuous increase of the shear value.
It is interesting to note that the strain glass state was discovered when people were seeking answers to the experimentally observed abnormal electrical resistivity change in the so-called nontransforming NiTi-based alloys (63,65,66). Due to the disappearance of heat flow peaks in DSC curves, it was assumed that there is no transformation in TiNi and TiNiFe systems when the doped Ni and Fe concentrations, respectively, are high. If there are no phase transformations in metals, their electrical resistivity should decrease with decreasing temperature. However, the electrical resistivity of these systems shows abnormal increases upon cooling (63,65,66). This abnormal electrical resistivity increase has been thought to be associated with the appearance of a precursory martensitic phase, but no normal martensitic transformation has been reported upon further cooling. The R martensitic phase in these alloys has higher electrical resistivity than that of the B2 parent phase. Thus, the abnormal electrical resistivity increase with decreasing temperature must be related to the B2 to R transformation, which has been proved to be a strain glass transition that produces R-phase nanodomains in the doped TiNi and TiNiFe systems (25,34). The continued nucleation and growth of R martensitic nanodomains upon cooling lead to an abnormal increase in the electrical resistivity. Experimental observations have shown that the temperature range in which the abnormal electrical resistivity is observed is consistent with the temperature range in which the frequency dispersion of the storage modulus occurs and the divarication of the zero-field-cooling and field-cooling curves starts. In particular, the electrical resistivity has shown a continuous increase with zero thermal hysteresis upon cooling and heating, which is different from how the electrical resistivity changes during normal B2 ⇋ R martensitic transformation (85). The inflection point on the electrical resistivity curves upon cooling at high temperature is related to the special temperature, T nd , at which stable martensite nanodomains start to appear, while the inflection point at low temperature is related to T g (25). Note that the strain glass transition with B19 ′ local structure shows a continuously decreasing electrical resistivity upon cooling, which is due to the lower value of electrical resistivity of the B19 ′ phase compared to that of the B2 phase (86).
According to the above experimental measurements, phase diagrams of different strain states, including strain liquid (i.e., the parent phase), strain crystal (i.e., the normal martensite phase), strain glass, and transitions among them, have been established in different SMAs (6,25,26,34,35,44). Figure 1 shows such a phase diagram. At low defect concentrations, there exist normal martensitic transformations between strain liquid and strain crystal, with the formation of microscale, internally twinned martensite upon cooling. At high defect concentrations, however, such martensitic transformations are replaced by strain glass transitions with continuously freezing-in martensitic nanodomains. Besides the martensitic transformations and strain glass transitions shown in Figure 1, further experiments and simulations have shown that the phase boundary between the strain crystal and strain glass is not vertical but tilted and is not a single line but a region, which indicates a narrow concentration range in which strain glass transition and martensitic transformation could coexist (32,70,71,80,87). Within this concentration range, the systems show the coexistence of microscale, long-range ordered, internally twinned martensitic plates at some local regions and martensitic nanodomains at some other local regions. The DMA measurement shows two peaks for the storage modulus and internal friction, and the XRD results show the conventional peak for the martensitic phase (32,70).
Above T g at a high defect concentration or above M s at a low defect concentration and below T nd (see Figure 1), there exists a precursory strain state over a wide concentration range. This partially frozen state contains both static (frozen) and dynamic (unfrozen) nanodomains of martensite. The dynamic nanodomains of martensite, which can further transform into normal martensite, are also called tweed structure in systems with large elastic anisotropy (19,88). Thus, in a ferroelastic system, the phase transitions change from a strong first-order martensitic transformation to a continuous strain glass transition with increasing defect concentration. Different defect types will create different amounts of lattice distortions and alter the phase boundaries in the phase diagram (23,49). For example, 1.5% excess Ni is required in NiTi and 6% Fe is required in NiTi-Fe to induce a similar strain glass transition.
The establishment of strain glass phase diagrams has expanded the theory of phase transformations in ferroelastic systems and could provide (a) a new angle from which to look at some long-standing, unresolved issues, such as nearly linear SE, the disappearance of normal martensitic transformation heat flow peaks, and Invar and Elinvar anomalies, and (b) useful guidance for defect engineering to achieve desired strain domain patterns for controlled strain release.
Because of the continuous transition characteristic, strain glass systems have well-controlled strain release during deformation and may offer many unique properties, such as linear SE with nearly zero hysteresis (69), excellent thermal cycling properties with strong fatigue resistance (30), and Invar and Elinvar anomalies (5,6).
Figure 5a shows a typical example (30) of nearly linear SE (no strain avalanche) with a slim hysteresis and high strength over a wide temperature range, which has been observed in most strain glass systems. Continuous elastic modulus softening upon cooling associated with the strain glass transition compensates for the normal modulus hardening upon cooling and leads to the Elinvar anomaly (5, 7, 89) (see, e.g., Figure 5b), while tunable strain release of strain glass transition leads to a tunable thermal expansion coefficient that is positive, negative, or close to zero (i.e., the Invar phenomenon) (6, 90, 91) (see, e.g., Figure 5d). Large magnetostriction has also been reported in the Fe-Pd strain glass system (see Figure 5c), which is caused by the ease with which martensitic nanodomains switch (45,92). SE with low modulus could have important applications in accurate control of microelectromechanical systems and pediatric implants, the wide temperature range for SE may be suitable for space exploration, and Invar and Elinvar strain glasses can be used in high-precision instruments. Note that strain glasses in NiTi SMAs also show normal SME and SE with large hysteresis at low temperatures (approximately 173 K), which can be attributed to stress-induced R strain glass to B19 ′ martensite transition (93).
In experiments, strain glass has shown unique nanoscale martensitic domains and continuous transition behavior, and it is believed that defects play an important role in regulating the transition behavior and producing disordered strain state. To explain the physical origin of strain glass transition and nanoscale martensitic domains, many models, from atomic scale to mesoscopic scale, are reviewed in the following sections.
To understand the experimentally observed unique phenomena and properties associated with strain glass transition, several models have been proposed that consider the local stress field caused by random point defects; local concentration and stress fields generated by nanoprecipitates; the elastic anisotropy of different systems; the strain network created by different defects including point defects, dislocations, and nanoprecipitates; and other characteristics (23,24,47,68,94). Adding random, stress-carrying defects could interrupt the formation of long-range ordered transformation strain patterns because a random stress field is incompatible with the long-range ordered, self-accommodating strain patterns produced by normal martensitic transformations via autocatalysis. In addition, local solute concentration variations associated with either impurity doping, spinodal decomposition, precipitation, and segregation at extended defects create thermodynamic stability (i.e., M s ) variations. As a consequence, different locations in the system start the martensitic transformation at different temperatures or stress levels, with isolated nanodomains of martensite formed in regions with high M s being confined by the surrounding parent phase matrix that has higher stability (58,68,95). This also suppresses the autocatalysis and smears the martensitic transformation into a strain glass transition. Furthermore, the stress-free transformation strain and elastic anisotropy of the system itself also influence how easily strain glass forms (47,48,96). A smaller transformation strain or lower elastic anisotropy requires a lower defect concentration or a weaker local field at a fixed defect concentration, and a larger transformation strain or a higher elastic anisotropy requires a higher defect concentration or a stronger local field at a fixed defect concentration, to convert normal martensitic transformations into strain glass transitions.
Phase field modeling based on Landau theory of phase transformations has been used widely in the study of martensitic transformations (97,98) and strain glass transitions (23,68,69), which can incorporate easily both the chemical and mechanical effects discussed above [i.e., effects from concentration and stress fields associated with various point defects (22,47,49,68,94,(99)(100)(101) and extended defects such as nanoprecipitates (27,28,55,58,102,103) and dislocations (61,(104)(105)(106)(107)]. The total free energy of the system in the phase field model consists of four parts:
where f ch is the chemical free energy density, which is usually approximated by a Landau polynomial (94,97),
where r is the spatial coordinate, c is the point defect concentration, T is the temperature, η p (r)(p = 1, 2, ..., n) are the structural order parameters that characterize the martensitic phase with stress-free transformation strain of the p th variant from total n variants,
T 0 (c) = T 00 + bc with T 00 being the phase transition temperature of a defect-free system, and b is a constant that characterizes the concentration effect on the transition temperature. The excess energy density f L associated with a local stress field generated by defects is characterized by (68,69)
where σ L (r) is the local stress field created by defects [which has different forms for different types of defects, such as point defects (substitutional and interstitial point defects may also assume different forms), dislocations, and coherent precipitates] and ε(r) is the strain field associated with the martensitic domains described by the structural order parameters η p (r) and the stress-free transformation strain ε 00 p [i.e., ε(r) = n p ε 00 p (r)η 2 p (r)] (68, 97, 98). Also, f gr is the gradient energy density associated with structural heterogeneity characterized by η p (r), f gr = 1 2 β( n p ∇η p ) 2 ,where β is the gradient energy coefficient, and E el contains the coherency elastic strain energy and work term by external stress, which can be described by Khachaturyan's microelasticity theory (97,98):
where C ijkl is the elastic constant tensor, k is the wave vector defined in the reciprocal space, {η 2 p (r)} k is the Fourier transform of η 2 p (r), {η 2 q (r)} * k is the complex conjugate of η 2 q (r)andB pq (e) = e i σ 0 ij (p) jk σ 0 kl (q)e l , σ 0 ij (p) = C ijkl ε 00 ij (p), -1 = C ijkl e k e l ,andσ appl is the applied external stress. The microstructural evolution during martensitic transformation is then characterized by the time-evolution of the structural order parameters, η p (r), following the time-dependent Ginzburg-Landau equation:
where L is the kinetic coefficient characterizing domain wall motion and ξ is the Langevin noise term describing thermal fluctuations.
The first strain glass system discovered and most of the strain glass systems reported so far are strain glasses created by point defect doping. Similar to the effects of point defect doping on the formation of spin glasses and relaxors in ferromagnetics and ferroelectrics, point defect doping also has strong impacts on M s , martensitic transformation product, and martensitic transformation path in ferroelastic systems (14). Three important effects from random point defects on martensitic transformation have been identified (68,94,95). The first is the global transition temperature effect (GTTE) associated with alloy composition change by point defect doping, which influences the overall transition temperature of the alloy as a whole. 3, and can be characterized by the elastic interaction between a martensitic domain characterized by its transformation strain ε 00 p , order parameter η p , and the local stress field σ L created by the point defects. Figure 6a shows the effects of the LFE from lattice distortion caused by a point defect.
Phase field simulations (23,68,69) based on the above established Landau free energy model could describe the formation of martensitic nanodomains, zero-field-cooling/field-cooling curves, frequency dispersion, and continuous transition behavior of strain glass transitions (23,68,69). Based on the simulation results, phase diagrams of the strain glass systems studied have been established (23,68) that are consistent with the phase diagram shown in Figure 1 and experimentally determined ones (25,26,34). Figure 6b shows an example of 2D phase field simulation results of martensitic transformation and strain glass transition in a model system that has a cubic to tetragonal martensitic transformation. When the defect concentration is low (c = 0.0-0.1), the system shows a normal martensitic transformation that produces long-range ordered twinning martensite. However, when the defect concentration exceeds a critical value (e.g., c = 0.125 in this example), the long-range ordered twin structures are replaced by frozen tweed structures consisting of nanodomains of individual martensitic variants (a typical strain glass microstructure). The nanodomain size decreases with increasing defect concentration. for B2 to R martensitic transformation in Ti 50 Ni 50 and B2 to R strain glass transition in Ti 50 Ni 44 Fe 6 , respectively, upon cooling and heating (69). The normal martensitic transformation in Figure 6c shows a sudden appearance and rapid growth of martensite into a long-range ordered, internally twinned, herringbone structure within a narrow temperature range upon cooling. These martensitic twin structures transform to austenite at a higher temperature upon heating, leading to a large hysteresis. However, the strain glass transition in Figure 6d shows continuous appearance/disappearance and slow growth/shrinking of individual martensitic domains over a wide temperature range upon cooling/heating, with a nearly vanishing hysteresis.
The critical value of defect concentration for separating martensitic transformation and strain glass transition may change as the type of point defect (e.g., substitutional versus interstitial, impurities of different atomic sizes and different chemical similarities to the host atoms) changes. In the NiTi-Cu system, for example, doping approximately 15% Cu still cannot suppress normal B2 to B19 martensitic transformation, while doping 7% Ni is enough to change B2 to B19 martensitic transformation to B2 to R strain glass transition with the formation of R-phase nanodomains (35). These subtle differences could be captured by adjusting their chemical and mechanical effects in the Landau free energy model discussed in Section 3.1.1. Among GTTE, LTTE, and LFE, the latter seems to play the most important role in suppressing autocatalysis, interrupting long-range ordered strain domain patterns assumed by self-accommodation among different martensitic variants, and turning a normal martensitic transformation into a strain glass transition (49). This is because self-accommodation and autocatalysis are all caused by long-range elastic interactions among different martensitic variants (i.e., mechanical in origin), and LFE (also mechanical in origin) makes its own variant selection that is most likely incompatible with the variant selection process by self-accommodation. Thus, among the three effects, the LFE provides the strongest suppression field resisting the formation of long-range ordered domain patterns. For example, cold rolling alone (in which only the LFE associated with dislocations is present) can make B19 ′ (approximately 10% transformation strain) strain glass transition in NiTi (30), while point defect doping alone (in which GTTE, LTTE, and LFE are present, but the LFE is rather weak) can only make R-phase (approximately 1% transformation strains) strain glass in NiTi-based SMAs, regardless of the defect concentrations (25,26,34,108). Thus, weak LFE caused by point defects cannot induce the formation of strain glass with large transformation strains such as B19 or B19 ′ strain glasses. To design strain glasses with giant superelastic strains, stronger LFE from extended defects such as dislocations is required (49). However, large and asymmetrical (nondilatational) lattice distortions caused by interstitial atoms can produce strain glass with intermediate transformation strain (approximately 2.6%)-for example, in oxygendoped TiNb-based alloys (6, 59, 109).
Since the order parameter of strain glass is the transformation strain, the long-range elastic interactions between nucleating martensitic domains and defects as well as among different martensitic domains themselves play a dominant role in the energetics of strain glass formation, which is similar to the case of normal martensitic transformations. In particular, the interplay among the activation energy barrier for nucleation of a single, non-self-accommodated martensitic variant at defects, the activation energy barrier for the formation of a self-accommodating multivariant martensitic twin, and the local chemical driving force for martensitic transformation determines the thermal stabilities of strain glass, strain crystal, and strain liquid.
Reference 47 reported that the elastic anisotropy of a system could influence the transformation strain domain patterns, as shown in Figure 7. The elastic anisotropy factor A can be defined as
The decrease of elastic anisotropy A 3 could change the martensitic transformation behavior and microstructural evolution. Figure 7 shows that a high elastic anisotropy could favor the formation of tweed at high temperature and long-range ordered twinning martensite at low temperature (88,110), while a low elastic anisotropy prefers the formation of nanodomains [i.e., a strain glass state (18,19)]. However, a pure martensitic system with elastic isotropy alone cannot produce strain glass (98); randomly distributed defects with enough concentration are still necessary. The anisotropy may change the value of the critical defect concentration required to form a strain glass, which is similar to the effect of different types of point defects. small. For example, although R, B19, and B19 ′ martensitic phases have been observed in NiTibased systems, only R-phase (trigonal) strain glass has been reported by doping point defect (25,26,34). No B19 or B19 ′ strain glasses can be generated by doping point defects in NiTi-based SMAs. This is because the transformation strains of the B19 (approximately 8%) and B19 ′ (approximately 10%) phases are much larger than that of the R phase (approximately 1%) (14). Point defects create limited lattice distortions with weak LFE, which cannot suppress the autocatalytic nucleation and growth of B19 or B19 ′ martensitic domains. Now the question is whether stronger defects could make B19 or B19 ′ strain glasses. Like point defects, extended defects such as dislocations, precipitates, and grain boundaries could also produce local composition variations and lattice distortions, which should show LTTE and LFE. However, unlike point defects, whose LFE is rather limited, the LFE associated with extended defects could be much stronger. Densely populated dislocations, deformation twins, and amorphous domains have been observed in severely cold-worked NiTi SMAs (111,112), which have indeed resulted in the change from a normal B2 to B19 ′ martensitic transformation to a B2 to B19 ′ strain glass transition (29,30). Such a B19 ′ strain glass has shown a much larger recoverable strain (4%) within a wide temperature range (30) compared to that of the R strain glass (0.5%) (69). This can be attributed to the large transformation strain (approximately 10%) of the B19 ′ martensite. Local stress fields created by dislocations could induce martensitic embryos at temperatures above the M s of the non-cold-rolled samples. For example, phase field simulations have shown that the stress/strain network created by dislocations produces embryonic martensitic domains at dislocations (61,105). Figure 8 shows the evolution of the martensitic domains under loading for a sample that has been plastically deformed to 5% strain before the loading, where martensitic domains exist above M s and continue to grow upon loading. To be able to suppress autocatalysis completely and turn a normal B19 ′ martensitic transformation into a B19 ′ strain glass transition, a critical amount of cold work (i.e., a critical dislocation density) is required (61,105).
In addition to dislocations, deformation twin boundaries were also found to have the ability to harbor martensitic embryos (113)(114)(115). These martensitic embryos induced by dislocations and deformation twins could grow instantaneously and continuously upon cooling/loading without the need for overcoming the activation energy barrier for nucleation, which reduces the hysteresis and increases the temperature range for SE (60,61). Thus, dislocations and deformation twins could be more effective defects to produce strain glasses in different SMAs due to their strong LFE. Stress and temperature cycling of SMAs could also produce dislocations and deformation twins, which significantly impact the martensitic transformation behavior (116)(117)(118). For SE in SMAs, the critical stress for a stressinduced martensitic transformation has to be lower than that of stress-induced dislocation slip (14). The dislocations and deformation twins introduced by cold work and stress/temperature cycling increase the strength of the parent phase and hence enhance the SE of a strain glass system.
Precipitate phases having different structures and compositions from the parent matrix phase could influence the martensitic transformation path and martensitic transformation temperature because the precipitation reactions generate composition heterogeneity at the scale of the growing precipitates and the local stress field (for coherent precipitates) and impose geometrical confinement (since the precipitates do not transform) (55,56,103,(119)(120)(121). In NiTi-based SMAs, Ni 4 Ti 3 precipitates can induce R phase and improve SE through strengthening the matrix (56,121,122), but no strain glass state or nano-sized martensitic domains have been reported in these alloys. As discussed in Section 2, the density of precipitates should play an important role in strain glass formation. The size and density of precipitates depend on alloy composition and aging temperature and time. Recent experimental work has shown that nanoprecipitates with high density by aging at a low temperature for a short time could induce strain glasses (27,28). Unfortunately, such nano-sized precipitates in NiTi SMAs can only induce strain glasses with local R structure. The lattice distortion caused by the precipitates is insufficient to induce B19 or B19 ′ strain glasses.
3.1.5. Atomic-scale understanding of strain glass transition. The above Landau theory is phenomenological, and the corresponding phase field simulations are at mesoscale. To gain a fundamental understanding of strain glass transition at the atomic scale, atomistic simulations are desired. Molecular dynamics (MD) simulations of phase transformations in NiTi systems have shown strain glass transition at high defect concentration, revealing that lattice distortion created by the Ni-Ni and Ni-Ti nearest neighbor atomic pairs at high antisite Ni concentrations leads to the suppression of autocatalysis and converts the martensitic transformation into a strain glass transition. The radial distribution functions of the bond length of Ni-Ni and Ni-Ti atomic pairs in a frozen strain glass state are closer to those in the martensitic phase, while the corresponding radial distribution functions in the unfrozen strain nanodomain states (i.e., tweed) are similar to those in the austenitic phase (123). In addition, first-principle calculations also suggest that the strain glass state may not be created by transformation strain pinning by point defects but rather by a disruption of the underlying electronic instability due to lattice expansion caused by the point defects (Co randomly substitutes Ni in this study) (124). Co atoms on the Ni sublattice lead to the formation of resonance (local) states and disrupt Fermi surface nesting.
Furthermore, the formation of strain glass has been attributed to the gradual percolation of local strain clusters (23,24). Point defects create localized strain clusters that expand and reach a percolation threshold at the glass transition temperature (i.e., the strain clusters form a percolated strain network) as the defect concentration increases. For example, it has been shown that the local strain field created by point defects first forms isolated strain islands at high temperatures (Figure 9a, subpanel i). Upon cooling, these islands expand to anisotropic shape (due to elastic anisotropy) and form a percolated strain network (Figure 9a, subpanel ii), which constrains the nucleation and growth of martensitic domains at a low temperature, as shown in Figure 9a, subpanel iv. Further studies suggested that this strain network can interrupt the formation of long-range ordered strain domains such as those seen in internally twinned martensite because the so-called strain network is not compatible with the self-accommodating strain domain patterns. This effect can be quantified by calculating the suppression field through the elastic interaction energy [ f p L (r)] between the p th variant of the martensite formed and the local stress field from the defects. The energetic criterion of the suppression field, f sup = f p L (r) + f ch (r), that determines whether a p th martensitic variant could form and grow, can be written as f p L (r) + f ch > 0, or f p L (r) + f ch (r) > f q L (r) + f ch (r), (p = q), where f ch (r) is the chemical driving force for the martensitic transformation (23). This means that either the parent phase or other variants of the martensitic phase will be more stable and the formation of the p th martensitic variant at the location will be prohibited (suppressed) when the criterion is satisfied. The volume fraction of such a suppression field depends on temperature, defect concentration, and defect strength, as shown in Figure 9b. The volume fraction of the suppression field for 3D percolation is approximately 0.68, which has predicted well the critical defect concentrations and glass transition temperatures in strain glass systems doped with different point defects (23).
As a newly discovered disordered state in ferroelastic systems, strain glass still prompts many unanswered questions. For example, suppression of autocatalysis by defects has been identified as the key to converting a normal martensitic transformation into a strain glass transition. However, (a, i and ii) The formation of a strain network upon cooling. The point defects induce the strain cluster, and the strain clusters grow and form a percolated strain network. The orange circles represent the strain cluster caused by doped defects; the red, orange, and blue colors inside of the dashed circles represent the central effective dopant and other cluster atoms at high and low temperatures; r e represents the radius of the strain cluster caused by defect. (a, iii and iv) Results of molecular dynamics simulations of ZrNi with atomic structures of strain glass with martensitic phase (yellow), parent phase (blue), and dopant atoms (red). (b) The required point defect concentrations for the percolation of a suppression field (that prevents the formation of given martensitic variants) at different temperatures, which is given by the intersections between the solid and dashed lines. Abbreviations: BCC, body-centered cubic; HCP, hexagonal close packed. Panel a adapted with permission from Reference 24; copyright 2020 American Physical Society. Panel b adapted with permission from Reference 23; copyright 2020 Elsevier.
direct ab initio and MD simulations of a strain glass transition are still lacking. Is the percolation threshold of a suppression field a good predictor of strain glass transition? In experiments, nanodomains of individual variants are observed in different strain glass systems, while in computer simulations, nanodomains of twinning martensite are also shown to have the unique properties of a strain glass transition. Are single-variant nanodomains of martensite necessary to define a strain glass state? The B19 ′ strain glass has shown a nearly linear SE with high strength (1.2 GPa), large recoverable strain (4%), and low elastic modulus (approximately 30 GPa) (30). Are these the optimal properties that one could achieve? What is the limit of the recoverable strain of a strain glass transition for a given stress-free transformation strain of the martensitic transformation? What is the lower limit of the apparent elastic modulus that could be achieved by a strain glass transition? Since strain glasses have nearly linear SE with slim hysteresis and high strength, excellent dimensional stability and functional fatigue resistance during stress or temperature cycling are expected. But both experimental and simulation studies are still lacking. Finally, the β relaxation is a general phenomenon in polymer and metallic glasses (125,126), but there is no report of such a relaxation in strain glasses or ferroic glasses.
The unique properties of strain glass transition are not surprising because it is similar to other nanostructured materials such as nanocrystalline materials (127), nanoscale multilayers (128), nanoprecipitates (129), nanoferromagnetic domains (130), nanopolarization domains (131), and nanocomposites (132), which are supposed to have unique properties compared to their microscale domain counterparts (133). Nanoscale martensitic domain engineering is the key to creating strain glass states and strain glass transitions. When each of the nanodomains can grow and produce local strains, a huge population of them will produce a large overall strain output. However, the random selection of variants by random fields associated with random defects will offer a limited amount of strain release. Thus, selection of only preferred variants by specially engineered defects or structural heterogeneities (such as deformation twins) for maximum strain output by strain glasses is highly desired. In situ TEM observations of stabilized martensitic domains by defects and the growth of these domains under applied load or upon cooling are also highly desired.
The insights gained by studying strain glass transition are beneficial to the design and optimization of other transforming materials (i.e., to use phase transformation to tailor materials properties), such as conventional SMAs (14,(134)(135)(136)(137), transformation-induced plasticity/ twinning-induced plasticity steels (138)(139)(140), and transformation-induced plasticity/twinninginduced plasticity Ti-alloys (141)(142)(143). In particular, concentration modulation-induced phase stability engineering (58), additive manufacturing (144,145), accumulative roll bonding (146), multilayer deposition, and other new processing techniques could be used to tailor the structural phase transformations for controlled strain release and thus desired properties.
Strain glass is a new strain state in ferroelastic materials characterized by nanodomains of martensite. These nanodomains are created and confined by heterogeneous stress field and/or composition field at the nanoscale associated with random defects, including (but not limited to) point defects, dislocations, deformation twins, and precipitates, or by nanoscale concentration modulations produced by (but not limited to) spinodal decomposition, precipitation reaction, and multilayer deposition. When such heterogeneous fields percolate, they completely suppress autocatalysis and self-accommodation among different martensitic variants, as these fields are incompatible with long-range ordered, self-accommodating transformation strain domain patterns generated by normal martensitic transformations. As a consequence, the nanodomains of martensite cannot evolve into microscale twinning martensite such as the herringbone structure (i.e., a strain crystal state in normal martensite) upon cooling and are frozen into a strain glass state. Such a strain glass state has a few fundamental characteristics: its average structure is the same as that of the parent phase, it shows frequency dispersion in the storage modulus or internal friction, and it exhibits continuous splitting of zero-field-cooling and field-cooling curves.
The characteristics of a strain glass transition and all the unique properties associated with it are determined by how the nanodomains respond to an external field, either stress or temperature. Because the random defects have a broad distribution of potency to trigger locally martensitic transformation, the martensitic transformation starts and finishes at much higher temperatures or lower stresses in some local regions and at much lower temperatures or much higher stresses in other local regions. Because of the confinement from neighboring regions that are nonaccommodating, the growth of the nanodomains is limited for a given amount of undercooling or increment of the applied load. Collectively, these effects lead to an overall continuous transformation, with the disappearance of heat flow in DSC measurements, continuous electrical resistivity change, and continuous elastic modulus softening. Because strain glass transition is diffusionless, its response to the external field is instantaneous. Thus, such a continuous transformation offers many unique properties, including nearly linear SE with large recoverable strain and slim hysteresis, ultralow elastic modulus with a broad temperature range, and Invar and Elinvar anomalies.
The key to creating a strain glass state is to engineer nanodomain structures of transformation strains (i.e., martensitic variants) by introducing internal random fields, either chemical or mechanical, with spatial variations at the nanometer scale. Point defect doping is an effective way to create strain glasses with relatively small transformation strains (a few present), such as the R phase. For martensitic systems with large transformation strains (approximately 10%), such as the B19 and B19 ′ phase, extended defects carrying much larger lattice distortions such as dislocations are required. For ferroelastic systems whose martensitic transformation temperature or stress is a strong function of alloy composition, creating nanoscale concentration modulations could be an effective way to engineer strain glasses as well.
The strain glass state and strain glass transition extend the theory of martensitic transformations, and a complete phase diagram of martensitic transformation plus strain glass transition in a ferroelastic system provides a blueprint in engineering strain domain microstructures by defect engineering for desired strain release.
Wang et al.
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Wang et al.
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