A multicaloric cooling cycle that exploits thermal hysteresis.

The giant magnetocaloric effect, in which large thermal changes are induced in a material on the application of a magnetic field, can be used for refrigeration applications, such as the cooling of systems from a small to a relatively large scale. However, commercial uptake is limited. We propose an approach to magnetic cooling that rejects the conventional idea that the hysteresis inherent in magnetostructural phase-change materials must be minimized to maximize the reversible magnetocaloric effect. Instead, we introduce a second stimulus, uniaxial stress, so that we can exploit the hysteresis. This allows us to lock-in the ferromagnetic phase as the magnetizing field is removed, which drastically removes the volume of the magnetic field source and so reduces the amount of expensive Nd-Fe-B permanent magnets needed for a magnetic refrigerator. In addition, the mass ratio between the magnetocaloric material and the permanent magnet can be increased, which allows scaling of the cooling power of a device simply by increasing the refrigerant body. The technical feasibility of this hysteresis-positive approach is demonstrated using Ni-Mn-In Heusler alloys. Our study could lead to an enhanced usage of the giant magnetocaloric effect in commercial applications.

Colossal Elastocaloric Effect in Ferroelastic Ni-Mn-Ti Alloys.

Energy-efficient and environment-friendly elastocaloric refrigeration, which is a promising replacement of the conventional vapor-compression refrigeration, requires extraordinary elastocaloric properties. Hitherto the largest elastocaloric effect is obtained in small-size films and wires of the prototype NiTi system. Here, we report a colossal elastocaloric effect, well exceeding that of NiTi alloys, in a class of bulk polycrystalline NiMn-based materials designed with the criterion of simultaneously having large volume change across phase transition and good mechanical properties. The reversible adiabatic temperature change reaches a strikingly high value of 31.5 K and the isothermal entropy change is as large as 45 J kg^{-1} K^{-1}. The achievement of such a colossal elastocaloric effect in bulk polycrystalline materials should push a significant step forward towards large-scale elastocaloric refrigeration applications. Moreover, our design strategy may inspire the discovery of giant caloric effects in a broad range of ferroelastic materials.

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials.

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO_{2}) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.

Statistical similarity between the compression of a porous material and earthquakes.

It has long been stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallels between these so separate phenomena. We study the acoustic emission events produced during the compression of Vycor (SiO(2)). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate.

Giant solid-state barocaloric effect in the Ni-Mn-In magnetic shape-memory alloy.

The search for materials showing large caloric effects close to room temperature has become a challenge in modern materials physics and it is expected that such a class of materials will provide a way to renew present cooling devices that are based on the vapour compression of hazardous gases. Up to now, the most promising materials are giant magnetocaloric materials. The discovery of materials showing a giant magnetocaloric effect at temperatures close to ambient has opened up the possibility of using them for refrigeration. As caloric effects refer to the isothermal entropy change achieved by application of an external field, several caloric effects can take place on tuning different external parameters such as pressure and electric field. Indeed the occurrence of large electrocaloric and elastocaloric effects has recently been reported. Here we show that the application of a moderate hydrostatic pressure to a magnetic shape-memory alloy gives rise to a caloric effect with a magnitude that is comparable to the giant magnetocaloric effect reported in this class of materials. We anticipate that similar barocaloric effects will occur in many giant-magnetocaloric materials undergoing magnetostructural transitions involving a volume change.

Giant and Reversible Barocaloric Effect in Trinuclear Spin-Crossover Complex Fe3 (bntrz)6 (tcnset)6.

A giant barocaloric effect (BCE) in a molecular material Fe3 (bntrz)6 (tcnset)6 (FBT) is reported, where bntrz = 4-(benzyl)-1,2,4-triazole and tcnset = 1,1,3,3-tetracyano-2-thioethylepropenide. The crystal structure of FBT contains a trinuclear transition metal complex that undergoes an abrupt spin-state switching between the state in which all three FeII centers are in the high-spin (S = 2) electronic configuration and the state in which all of them are in the low-spin (S = 0) configuration. Despite the strongly cooperative nature of the spin transition, it proceeds with a negligible hysteresis and a large volumetric change, suggesting that FBT should be a good candidate for producing a large BCE. Powder X-ray diffraction and calorimetry reveal that the material is highly susceptible to applied pressure, as the transition temperature spans the range from 318 at ambient pressure to 383 K at 2.6 kbar. Despite the large shift in the spin-transition temperature, its nonhysteretic character is maintained under applied pressure. Such behavior leads to a remarkably large and reversible BCE, characterized by an isothermal entropy change of 120 J kg-1 K-1 and an adiabatic temperature change of 35 K, which are among the highest reversible values reported for any caloric material thus far.

Magnetocaloric effect and its relation to shape-memory properties in ferromagnetic Heusler alloys.

Magnetic Heusler alloys which undergo a martensitic transition display interesting functional properties. In the present review, we survey the magnetocaloric effects of Ni-Mn-based Heusler alloys and discuss their relation with the magnetic shape-memory and magnetic superelasticity reported in these materials. We show that all these effects are a consequence of a strong coupling between structure and magnetism which enables a magnetic field to rearrange martensitic variants as well as to provide the possibility to induce the martensitic transition. These two features are respectively controlled by the magnetic anisotropy of the martensitic phase and by the difference in magnetic moments between the structural phases. The relevance of each of these contributions to the magnetocaloric properties is analysed.

Influence of the number of orientational domains on avalanche criticality in ferroelastic transitions.

We study the relationship between avalanche criticality and the number of orientational domains in ferroelastic transitions. To this end, we use a general Ginzburg-Landau model appropriate for displacive transitions of the square lattice. The model includes disorder as a quenched distribution of local transition temperatures. We focus on the square-to-rectangle and the square-to-oblique ferroelastic transitions, which have two and four orientational domains, respectively, which in turn determine the corresponding degeneracy of the ground state of the system. The phase transitions are driven by temperature under the assumption of a strict athermal behavior. That is, we assume that thermal fluctuations do not play any role. Numerical results are obtained using a purely relaxational dynamics, and it is shown that both the square-to-rectangle and the square-to-oblique transitions occur intermittently in the form of avalanches. Avalanche sizes and avalanche energies are found to display power-law distributions, which corroborates avalanche criticality. We compare and contrast the dependence of avalanche criticality on the number of orientational domains of the low-symmetry phase. It is found that the critical exponents depend on that number, in agreement with recent experimental results.

Criticality in failure under compression: Acoustic emission study of coal and charcoal with different microstructures.

A systematic study of acoustic emission avalanches in coal and charcoal samples under slow uniaxial compression is presented. The samples exhibit a range of organic composition in terms of chemical elements as well as different degrees of heterogeneity in the microstructure. The experimental analysis focuses on the energies E of the individual acoustic emission events as well as on the time correlations between successive events. The studied samples can be classified into three groups. The more homogeneous samples (group I) with pores in the micro and nanoscales, with signatures of hardening effects in the stress-strain curves, exhibit the cleanest critical power-law behavior for the energy distributions g(E)dE∼E^{-ε}dE with a critical exponent ε=1.4. The more heterogeneous samples with voids, macropores, and granular microstructures (group III), show signatures of weakening effects and a larger effective exponent close to the value ε=1.66, but in some cases truncated by exponential damping factors. The rest of the samples (group II) exhibit a mixed crossover behavior still compatible with an effective exponent ε=1.4 but clearly truncated by exponential factors. These results suggest the existence of two possible universality classes in the failure of porous materials under compression: one for homogeneous samples and another for highly heterogeneous samples. Concerning time correlations between avalanches, all samples exhibit very similar waiting time distributions although some differences for the Omori aftershock distributions cannot be discarded.

Avalanche mixing and the simultaneous collapse of two media under uniaxial stress.

Avalanches in coal and sandstone samples under common uniaxial stress serve as a model for mixing of avalanche exponents in ceramics, multiferroics, and alloys. The two media are sandwiched together and subjected to common uniaxial stress using high- and low-stress compression. Each medium collapses individually through avalanches that often coincide with secondary avalanches into the other medium. The total avalanche time sequence allows a detailed investigation of the mixing by superposition and delayed coincidence. Correlations can be described by an inter-media Båth's law.

Martensitic transformation B2-R in Ni-Ti-Fe: experimental determination of the Landau potential and quantum saturation of the order parameter.

The Landau potential of the martensitic phase transformation in Ni(46.8)Ti(50)Fe(3.2) was determined using high resolution x-ray diffraction to measure the spontaneous strain and calorimetric measurements to determine the excess specific heat of the R phase. The spontaneous strain is proportional to the square of the order parameter which is tested by the relation of the excess entropy and the order parameter. The parameters of the Landau free energy were determined by fitting the temperature evolution of the order parameter and using the scaling between the excess entropy and the order parameter. The double well potential at absolute zero temperature was calculated and the interface energy and domain wall thickness were estimated.

Avalanche criticality in thermal-driven martensitic transitions: the asymmetry of the forward and reverse transitions in shape-memory materials.

Martensitic transitions take place intermittently as a sequence of avalanches which are accompanied by the emission of acoustic waves. The study of this acoustic emission (AE) reveals the scale-free nature of the avalanches. In a number of shape memory materials undergoing a martensitic transition it has been found that, in spite of relatively low hysteresis, the dynamics of forward and reverse transitions are different, which may explain the fact that the AE activity is different in both forward and reverse transitions. The asymmetry could be a consequence of the fact that, while nucleation is required for the transition from the parent to martensitic phase to take place, reverse transition occurs by fast shrinkage of martensitic domains. We have analysed in detail the distribution of avalanches in cooling and heating runs in Fe-Pd and Cu-Zn-Al shape-memory alloys. In the former, the martensitic transition is weakly first order while it shows a significant first order character in the latter. We have found that in Fe-Pd the distributions are power law for the forward and reverse transitions characterized by the same critical exponents. For Cu-Zn-Al the distribution of avalanches is critical in forward transitions but exponentially damped in the reverse transition. It is suggested that this different behaviour could originate from the different dynamic mechanisms in forward and reverse transitions.

Materials with Giant Mechanocaloric Effects: Cooling by Strength.

The search for materials with large caloric effects has become a major challenge in material science due to their potential in developing near room-temperature solid-state cooling devices, which are both efficient and clean, and that can successfully replace present refrigeration technologies. There are three main families of caloric materials: magnetocaloric, electrocaloric, and mechanocaloric. While magnetocaloric and electrocaloric materials have been studied intensively in the last few decades, mechanocaloric materials are only very recently receiving a great deal of attention. The mechanocaloric effect refers to the reversible thermal response of a solid when subjected to an external mechanical field, and encompasses both the elastocaloric effect, corresponding to a uniaxial force, and the barocaloric effect, which corresponds to the response to hydrostatic pressure. Here, the state of the art in giant mechanocaloric effects is reviewed and a critical analysis of the thermodynamic quantities that characterize the major families of barocaloric and elastocaloric materials is provided. Finally perspectives for further development in this area are given.

Geometrical model for martensitic phase transitions: Understanding criticality and weak universality during microstructure growth.

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L×L and in the thermodynamic limit L→∞, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

Giant barocaloric effects over a wide temperature range in superionic conductor AgI.

Current interest in barocaloric effects has been stimulated by the discovery that these pressure-driven thermal changes can be giant near ferroic phase transitions in materials that display magnetic or electrical order. Here we demonstrate giant inverse barocaloric effects in the solid electrolyte AgI, near its superionic phase transition at ~420 K. Over a wide range of temperatures, hydrostatic pressure changes of 2.5 kbar yield large and reversible barocaloric effects, resulting in large values of refrigerant capacity. Moreover, the peak values of isothermal entropy change (60 J K-1 kg-1 or 0.34 J K-1 cm-3) and adiabatic temperature changes (18 K), which we identify for a starting temperature of 390 K, exceed all values previously recorded for barocaloric materials. Our work should therefore inspire the study of barocaloric effects in a wide range of solid electrolytes, as well as the parallel development of cooling devices.

Mechanocaloric effects in shape memory alloys.

Shape memory alloys (SMA) are a class of ferroic materials which undergo a structural (martensitic) transition where the associated ferroic property is a lattice distortion (strain). The sensitiveness of the transition to the conjugated external field (stress), together with the latent heat of the transition, gives rise to giant mechanocaloric effects. In non-magnetic SMA, the lattice distortion is mostly described by a pure shear and the martensitic transition in this family of alloys is strongly affected by uniaxial stress, whereas it is basically insensitive to hydrostatic pressure. As a result, non-magnetic alloys exhibit giant elastocaloric effects but negligible barocaloric effects. By contrast, in a number of magnetic SMA, the lattice distortion at the martensitic transition involves a volume change in addition to the shear strain. Those alloys are affected by both uniaxial stress and hydrostatic pressure and they exhibit giant elastocaloric and barocaloric effects. The paper aims at providing a critical survey of available experimental data on elastocaloric and barocaloric effects in magnetic and non-magnetic SMA.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'.

Thermodynamics of multicaloric effects in multiferroic materials: application to metamagnetic shape-memory alloys and ferrotoroidics.

We develop a general thermodynamic framework to investigate multicaloric effects in multiferroic materials. This is applied to the study of both magnetostructural and magnetoelectric multiferroics. Landau models with appropriate interplay between the corresponding ferroic properties (order parameters) are proposed for metamagnetic shape-memory and ferrotoroidic materials, which, respectively, belong to the two classes of multiferroics. For each ferroic property, caloric effects are quantified by the isothermal entropy change induced by the application of the corresponding thermodynamically conjugated field. The multicaloric effect is obtained as a function of the two relevant applied fields in each class of multiferroics. It is further shown that multicaloric effects comprise the corresponding contributions from caloric effects associated with each ferroic property and the cross-contribution arising from the interplay between these ferroic properties.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'.

Avalanche criticality during compression of porcine cortical bone of different ages.

Crack events developed during uniaxial compression of cortical bones cut from femurs of developing pigs of several ages (4, 12, and 20 weeks) generate avalanches. These avalanches have been investigated by acoustic emission analysis techniques. The avalanche energies are power-law distributed over more than four decades. Such behavior indicates the absence of characteristic scales and suggests avalanche criticality. The statistical distributions of energies and waiting times depend on the pig age and indicate that bones become stronger, but less ductile, with increasing age. Crack propagation is equally age-dependent. Older pigs show, on average, larger cracks with a time distribution similar to those of aftershocks in earthquakes, while younger pigs show only statistically independent failure events.