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The partially overlapped ferroelastic/martensitic and para-ferromagnetic phase transitions of a Ni$_{50.53}$Mn${33.65}$In$_{15.82}$ metamagnetic shape memory alloy have been studied from calorimetric, magnetic and acoustic emission measurement. We have taken advantage of the existence of thermal hysteresis of the first order ferroelastic/martensitic phase transition ($\sim2.5$K) to discriminate the latent heat contribution $\Delta$Ht = 7.21(15) kJ/kg and the specific heat contribution $\Delta$Hc = 216(1) J/kg to the total excess enthalpy of the phase transition. The specific heat was found to follow a step-like behavior at this phase transition. The intermittent dynamics of the ferroelastic/martensitic transition has been characterized as a series of avalanches detected both from acoustic emission and calorimetric measurements. The energy distribution of these avalanche events was found to follow a power law with a characteristic energy exponent $\epsilon\sim2$ which is in agreement with the expected value for a system undergoing a symmetry change from cubic to monoclinic. Finally, the critical behavior of the para-ferromagnetic austenite phase transition that takes place at $\sim 311$K has been studied from the behavior of the specific heat. A critical exponent $\alpha\sim0.09$ has been obtained, which has been shown to be in agreement with previous values reported for Ni-Mn-Ga alloys but different from the critical divergence reported for pure Ni., Comment: 18 pages, 11 figures

The first-order diffusionless structural phase transition in Cu67.64Zn16.71Al15.65 is characterized by jerky propagation of phase front related to the appearance of avalanches. In this work we describe a full analysis of this avalanche behaviour using calorimetric heat-flux measurements and the results are compared with acoustic emission (AE) measurements.

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 $L\ifmmode\times\else\texttimes\fi{}L$ and in the thermodynamic limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$, 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.

We study the giant elastocaloric effect in a Cu-Zn-Al shape-memory alloy by means of simultaneous calorimetry and dilatometry measurements under applied uniaxial compression which have been carried out with a bespoke experimental setup. The output data allow a unique quasidirect and indirect characterization of the thermal response that provides accurate ΔS and ΔT values. We report a large thermal response of |ΔS| = 22 J K kg−1, |ΔT| = 12.3 K, and RC = 325 K kg−1 driven by moderate uniaxial compression changes of 32.2 MPa, which is comparable with the performance of the best magnetocaloric materials. In view of the hysteresis effects, the thermal response is predicted to exhibit reversible values for |Δσ| = 32 MPa.

The effect of thermal cycling in the martensitic phase transitions of a Cu–Zn–Al single crystal shape-memory alloy has been studied by monitoring the acoustic activity generated during the transition. The correlation function between the acoustic activity of k and k + Δ k cycles has been computed for the whole transformation and for selected temperature intervals Δ T within the transition region. Results indicate that for the whole transition there is a learning process in which the system seeks an optimal path of its internal variables that connect the parent and the martensitic phases. The learning process in the central part of the transition dominates the global behaviour and is different from the behaviour in the early- and late-stages of the transition.

We have extended the degenerate BEG model[1] to include magnetic degrees of freedom in order to study the premartensitic effects in Ni 2 MnGa. The model is solved by using mean-field theory and Monte Carlo techniques [2]. The numerical simulations reveal the crucial importance of fluctuations in pretransitional effects. Moreover, we find that a large variety of premartensitic effects may appear due to the magnetoelastic coupling. For large values of the coupling parameter a first-order transition line ending in a critical point appears. This critical point is responsible for the existence of large premartensitic fluctuations which manifest as broad peaks in the specific heat, not always associated with a true phase transition. The main conclusion is that premartensitic effects result from the interplay between the softness of the anomalous phonon driving the modulation and the magnetoelastic coupling strength. In particular, the premartensitic transition occurs when such coupling is strong enough to prevent a complete softening of the involved phonon mode. The implication of the results in relation to the available experimental data is discussed.

A generalization of the Blume-Emery-Griffiths model is introduced in which an entropy stabilization of the high-temperature phase is controlled by a degeneracy parameter p >~ 1 . The model describes a first- and a second-order phase transition as a function of temperature between two ordered phases. This is relevant for the martensitic transition problem. Mean-field calculations and Monte Carlo simulations are presented. The model predicts a constant entropy change at the transition for various transition temperatures in agreement with the behavior found experimentally.

We have systematically analyzed six different reticular models with quenched disorder and no thermal fluctuations exhibiting a field-driven first-order phase transition. We have studied the nonequilibrium transition, appearing when varying the amount of disorder, characterized by the change from a discontinuous hysteresis cycle (with one or more large avalanches) to a smooth one (with only tiny avalanches). We have computed critical exponents using finite size scaling techniques and shown that they are consistent with universal values depending only on the space dimensionality d.

The acoustic emission associated with front propagation has been used to investigate the dynamics of a solid-solid martensitic phase transition. By using two sensors we have been able to locate the position of active fronts and to measure their associated energy release. The investigation of the reverse transitions occurring in a Cu-Zn-Al alloy from a stressed martensitic phase to a cubic phase at zero stress reveals significant differences in the front trajectories depending on whether the transition is driven by controlling the applied load (soft driving) or by controlling the elongation of the sample (hard driving). In agreement with theoretical predictions [F. J. P\'erez-Reche, L.Truskinovsky, and G. Zanzotto, Phys. Rev. Lett. 99, 075501 (2007)], we have observed different evolutions of the transition dynamics under cycling as well as other constrained kinetic effects.

We review several aspects of the dynamics of first-order phase transitions in functional materials. In particular, we focus on recent models of the athermal evolution in driven ferromagnets that provide a global picture of metastability and hysteresis, and show that first-order phase transitions in these systems proceed by avalanches. Within this theoretical framework, we discuss recent experiments on acoustic emission avalanches in structural phase transitions.

Domain growth dynamics in binary alloys undergoing an order-disorder phase transition is revised. After a summary of the state-of-the-art of the problem, we focus on the Monte Carlo simulation results. The usual atom-exchange dynamics is compared with a more realistic vacancy driven dynamics. Results suggest that the expected Allen-Cahn growth law might be modified by this more realistic dynamics.

We present a numerical study of the zero-temperature response of the Gaussian random-field Ising model to a slowly varying external field, allowing the system to be trapped in microscopic configurations that are not fully metastable. This modification of the standard single-spin-flip dynamics results in an increase in dissipation (hysteresis) somewhat similar to that observed with a finite driving rate. We then study the distribution of avalanches along the hysteresis loop and perform a finite-size scaling analysis that shows good evidence that the critical exponents associated to the disorder-induced phase transition are not modified.

Monte Carlo simulation of a two-dimensional lattice gas model of orientable particles is used to study the coupling between the smectic-nematic phase transition and the orientational order parameter in Liquid Crystals. The phase diagram of the model is obtained, and the critical behaviour of the smectic-nematic-like transition studied. Results can be qualitatively compared with experimental data and suggest a microscopical explanation of the continuous variation of the effective critical exponents in some Liquid Crystal mixtures. The existence of a Tricritical Point is also reproduced. Finally, results are analyzed in terms of a general Landau free energy functional (Anisimov et al 1990 Phys. Rev. A 41 6749) that suggests that the Tricritical Point is only apparent.

We have investigated the spin-glass phase of CuAlMn alloys with less than 10 at% Mn. The experimental data have been compared to the results obtained from a simulation of a diluted Ising spin-glass at T = 0 K. The model, in agreement with experiments, exhibits a disorder induced phase transition from a spin-glass phase with a smooth hysteresis cycle to a ferromagnetic phase with a much sharper cycle.

A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the Random Field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional (3D) microstructure formation and on avalanche statistics., Comment: 11 pages, 16 figures

Using a 2-D lattice gas model of orientable molecules that exhibits two phase transitions, we have performed Monte Carlo simulations in order to study its critical behaviour. One of the phase transitions, associated with positional degrees of freedom, has been found to be second order, while the other, related to orientational degrees of freedom, is first order. Changing the parameters of the hamiltonian we can vary the separation between the two phase transition temperatures. When they are very close to each other the β critical exponent (or at least the effective β critical exponent) of the positional transition varies continuously from the 2-D Ising value to zero when the two transitions overlap. The model is also suitable for qualitatively explaining some experimental results found in Liquid Crystals and other systems showing coupling effects between orientational and positional degrees of freedom.

We report on the existence of acoustic emission during the paramagnetic-monoclinic\ensuremath{\leftrightarrow}ferromagnetic-orthorhombic magnetostructural phase transition in the giant magnetocaloric ${\mathrm{Gd}}_{5}{\mathrm{Si}}_{2}{\mathrm{Ge}}_{2}$ compound. The transition kinetics have been analyzed from the detected acoustic signals. It is shown that this transition proceeds by avalanches between metastable states.

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T= 0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, historydependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches sin number and sized stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

We have studied the driving rate and temperature dependence of the power-law exponents that characterize the avalanche distribution in first-order phase transitions. Measurements of acoustic emission in structural transitions in Cu-Zn-Al and Cu-Al-Ni are presented. We show how the observed behaviour emerges within a general framework of competing time scales of avalanche relaxation, driving rate, and thermal fluctuations. We have confirmed our findings by numerical simulations of a prototype model., Comment: 4 pages, 3 figures

Measurements of magnetic hysteresis loops in Cu-Al-Mn alloys of different Mn content at low temperatures are presented. The loops are smooth and continuous above a certain temperature, but exhibit a magnetization discontinuity below that temperature. Scaling analysis suggest that this system displays a disorder induced phase transition line. Measurements allow to determine the critical exponents $\beta=0.03\pm 0.01$ and $\beta \delta = 0.4 \pm 0.1$ in agreement with those reported recently [Berger et al., Phys. Rev. Lett. {\bf 85}, 4176 (2000)], Comment: 4 pages, 5 figures

The significance of thermal fluctuations in nucleation in structural first-order phase transitions has been examined. The prototypical case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.

In the study of out of equilibrium relaxation phenomena two processes are considered as prototypes. Both correspond to the evolution of a solid AB binary alloy quenched from a high-temperature disordered phase to a temperature below a phase transition. The first case is the growth of ordered domains @nonconserved order parameter ~NCOP!# and the second is the phase separation problem @conserved order parameter ~COP!#. There is general agreement, 1 in the fact, that in both cases the mean size of the domains R grows, during the late stages of the evolution, following a power law. Such laws @R(t);t x # are characterized by the growth exponent x that takes the value x NCOP51/2 ~Allen-Cahn law 2 ! for the nonconserved case and x COP51/3 ~Lifshitz-Slyozov law 3 ! for the conserved case. These values are considered to be universal. They have been corroborated by theoretical arguments, numerical analysis of Langevin equations and Monte Carlo ~MC! simulations of lattice systems. 1 In this report we

We study isothermal magnetization processes in the Cu-Al-Mn intermetallic alloy. Hysteresis is observed at temperatures below the spin-freezing of the system. The characteristics of the hysteresis cycles as a function of temperature and Mn content (magnetic element) are obtained. At low temperature (5 K) a change from smooth to sharp cycles is observed with increasing Mn content, which is related to the decrease of configurational disorder. We also study a zero-temperature site-diluted Ising model, suitable for the description of this Cu-Al-Mn system. The model reproduces the main features of the hysteresis loops observed experimentally. It exhibits a disorder-induced critical line separating a disordered phase from an incipient ferromagnetic ground-state. The comparison between the model and the experiments allows to conclude that the observed change in the experimental hysteresis loops can be understood within the framework of the theory of disorder-induced criticality in fluctuationless first-order phase transitions., Comment: 30 pages, 15 eps figures, 2 tables. To appear Phys. Rev. B 59 (June 1999)

Acoustic emission avalanche distributions are studied in different alloy systems that exhibit a phase transition from a bcc to a close-packed structure. After a small number of thermal cycles through the transition, the distributions become critically stable (exhibit power-law behavior) and can be characterized by an exponent $\ensuremath{\alpha}$. The values of $\ensuremath{\alpha}$ can be classified into universality classes, which depend exclusively on the symmetry of the resulting close-packed structure.

Measurements of magnetic hysteresis loops performed at low temperatures on Cu–Al–Mn alloys with different Mn-content are presented. The loops are smooth and continuous above a certain temperature, while they exhibit a magnetization discontinuity below this temperature. Scaling analysis suggests that this system displays a disorder-induced phase transition line and allows determining the critical exponents (β=0.03±0.01 and βδ=13±3). Results indicate that by changing temperature, it is possible to tune the disorder responsible for the transition.

We present an experimental study of the transformation avalanches taking place during a thermally induced thermoelastic martensitic phase transition of a Cu-Zn-Al alloy. We have studied the statistical distribution of amplitudes and durations of the acoustic emission signals released in the avalanches and found them to exhibit power-law behavior in more than one decade. Distributions measured around different temperatures along the transformation path are found to be equivalent. We have measured the exponents for the distribution of amplitudes (\ensuremath{\alpha}=3.6\ifmmode\pm\else\textpm\fi{}0.8) and durations (\ensuremath{\tau}=3.5\ifmmode\pm\else\textpm\fi{}0.8), for the statistical dependence of amplitudes on durations (x=1.0\ifmmode\pm\else\textpm\fi{}0.1) and for the power spectrum of trains of measured acoustic signals (\ensuremath{\varphi}=0.9\ifmmode\pm\else\textpm\fi{}0.1).

Measurements of the Acoustic Emission generated during a Martensitic Transformation are presented. Statistical analysis of the amplitude and lifetime of signals has revealed power-law distributions for both magnitudes. The critical exponents of these distributions have been evaluated. The results are discussed in terms of modern theories of avalanche dynamics for first order phase transitions.

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

An important element in phase transitions occurring between different solid phases is the accommodation problem. The formed structure may not fit with its parent phase in respect to either the lattice constants or the symmetry. This gives rise to elastic deformations and large scale epitaxial rotations and twin formation. These phenomena are difficult to treat accurately by means of standard lattice gas models and Monte Carlo simulations. Here we shall describe a continuous Monte Carlo method and illustrate its capabilities on the simple test case of particles adsorbed with different coverage on a graphite surface. This is in fact closely related to an alloy problem, namely, that in which one of the elements (B) is represented by vacancies, which only interact via’ elastic forces’ originating from the interaction between the other elements (A), i.e. the adsorbate particles and their interaction with the parent phase, i.e. the substrate. As a test case this system is ideal since the’ elastic forces’ thereby are emphasized, and further in the sense that detailed experiments exists for comparison with calculated phase diagrams and structures, and finally that the system by definition is two dimensional, which makes it possible to study rather large systems by means of Monte Carlo simulations. This is in particular important when dealing with the effectively long ranged’ elastic interactions’ and the resulting twin domains of mesoscale dimensions. In this short paper only the method and a few examples can be given. More detailed results are given elsewhere (Vives and Lindgard 1991, 1992).

We study systems that can be described in terms of two kind of degrees of freedom when the corresponding ordering modes couple one to the other. The primary ordering mode gives rise to a diffusionless first-order phase transition and the secondary mode, that we suppose can be externally controlled, is associated to a continuous phase transition. Our interest is to analyze how the thermodynamic properties of the primary phase transition change as a function of the secondary ordering-mode. This can be experimentally realized in metallic alloys undergoing, at low temperatures, a martensitic phase transition and an order-disorder transition at much higher temperatures. In this case we obtain that, because of the directional character of the martensitic transition, the entropy-change dependence on atomic order is very small.

Direct observation of the entropy change in a first-order phase transition is obtained by using a differential scanning calorimeter in which the transition is field-induced under the application of an external magnetic field. This procedure enables direct evaluation of the magnetocaloric effect in materials showing first-order magnetostructural phase transitions. Results for Gd5(SixGe1−x)4 giant magnetocaloric alloys are reported. Calorimetric curves sweeping the field through the transition reveal a unusual increase of the entropy change with cycling. This increase is accounted for by considering both the structural and magnetic contributions to the total entropy change.

We report on experiments aimed at comparing the hysteretic response of a $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Zn}\text{\ensuremath{-}}\mathrm{Al}$ single crystal undergoing a martensitic transition under strain-driven and stress-driven conditions. Strain-driven experiments were performed using a conventional tensile machine while a special device was designed to perform stress-driven experiments. Significant differences in the hysteresis loops were found. The strain-driven curves show reentrant behavior (yield point) which is not observed in the stress-driven case. The dissipated energy in the stress-driven curves is larger than in the strain-driven ones. Results from recently proposed models qualitatively agree with experiments.

We consider systems that can be described in terms of two kinds of degree of freedom. The corresponding ordering modes may, under certain conditions, be coupled to each other. We may thus assume that the primary ordering mode gives rise to a diffusionless first-order phase transition. The change of its thermodynamic properties as a function of the secondary-ordering-mode state is then analyzed. Two specific examples are discussed. First, we study a three-state Potts model in a binary system. Using mean-field techniques, we obtain the phase diagram and different properties of the system as a function of the distribution of atoms on the different lattice sites. In the second case, the properties of a displacive structural phase transition of martensitic type in a binary alloy are studied as a function of atomic order. Because of the directional character of the martensitic-transition mechanism, we find only a very weak dependence of the entropy on atomic order. Experimental results are found to be in quite good agreement with theoretical predictions.

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

The existence of temporal correlations during the intermittent dynamics of a thermally driven structural phase transition is studied in a Cu–Zn–Al alloy. The sequence of avalanches is observed by means of two techniques: acoustic emission and high sensitivity calorimetry. Both methods reveal the existence of event clustering in a way that is equivalent to the Omori correlations between aftershocks in earthquakes as are commonly used in seismology.