Kinetics of martensitic transitions in Cu-Al-Mn under thermal cycling: Analysis at multiple length scales

In this paper we study the evolution of the kinetic features of the martensitic transition in a Cu-Al-Mn single crystal under thermal cycling. The use of several experimental techniques including optical microscopy, calorimetry, and acoustic emission, has enabled us to perform an analysis at multiple scales. In particular, we have focused on the analysis of avalanche events (associated with the nucleation and growth of martensitic domains), which occur during the transition. There are significant differences between the kinetics at large and small length scales. On the one hand, at small length scales, small avalanche events tend to sum to give new larger events in subsequent loops. On the other hand, at large length scales the large domains tend to split into smaller ones on thermal cycling. We suggest that such different behavior is the necessary ingredient that leads the system to the final critical state corresponding to a power-law distribution of avalanches.

Elastic constants of Ni-Mn-Ga magnetic shape memory alloys

We have measured the adiabatic second order elastic constants of two Ni-Mn-Ga magnetic shape memory crystals with different martensitic transition temperatures, using ultrasonic methods. The temperature dependence of the elastic constants has been followed across the ferromagnetic transition and down to the martensitic transition temperature. Within experimental errors no noticeable change in any of the elastic constants has been observed at the Curie point. The temperature dependence of the shear elastic constant C' has been found to be very different for the two alloys. Such a different behavior is in agreement with recent theoretical predictions for systems undergoing multi-stage structural transitions.

Martensitic transitions and the nature of ferromagnetism in the austenitic and martensitic states of Ni-Mn-Sn alloys

Structural and magnetic transformations in the Heusler-based system Ni0.50Mn0.50¿xSnx are studied by x-ray diffraction, optical microscopy, differential scanning calorimetry, and magnetization. The structural transformations are of austenitic-martensitic character. The austenite state has an L21 structure, whereas the structures of the martensite can be 10M , 14M , or L10 depending on the Sn composition. For samples that undergo martensitic transformations below and around room temperature, it is observed that the magnetic exchange in both parent and product phases is ferromagnetic, but the ferromagnetic exchange, characteristic of each phase, is found to be of different strength. This gives rise to different Curie temperatures for the austenitic and martensitic states.

Hysteresis in a system driven by either generalized force or displacement variables: martensitic phase transition in single-crystalline Cu-Zn-Al

We report on experiments aimed at comparing the hysteretic response of a Cu-Zn-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.

Cooling and heating by adiabatic magnetization in Ni50Mn34In16 magnetic shape-memory alloy

We report on measurements of the adiabatic temperature change in the inverse magnetocaloric Ni50Mn34In16 alloy. It is shown that this alloy heats up with the application of a magnetic field around the Curie point due to the conventional magnetocaloric effect. In contrast, the inverse magnetocaloric effect associated with the martensitic transition results in the unusual decrease of temperature by adiabatic magnetization. We also provide magnetization and specific heat data which enable to compare the measured temperature changes to the values indirectly computed from thermodynamic relationships. Good agreement is obtained for the conventional effect at the second-order paramagnetic-ferromagnetic phase transition. However, at the first-order structural transition the measured values at high fields are lower than the computed ones. Irreversible thermodynamics arguments are given to show that such a discrepancy is due to the irreversibility of the first-order martensitic transition.

Random-field Potts model with dipolarlike interactions: Hysteresis avalanches and microstructure

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 microstructure formation, and on avalanche statistics.

Liquid-gas phase transition in nuclear matter from realistic many-body approaches

The existence of a liquid-gas phase transition for hot nuclear systems at subsaturation densities is a well-established prediction of finite-temperature nuclear many-body theory. In this paper, we discuss for the first time the properties of such a phase transition for homogeneous nuclear matter within the self-consistent Green's function approach. We find a substantial decrease of the critical temperature with respect to the Brueckner-Hartree-Fock approximation. Even within the same approximation, the use of two different realistic nucleon-nucleon interactions gives rise to large differences in the properties of the critical point.

Dimensional reduction and gauge group reduction in Bianchi-type cosmology

In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-type cosmologies. We address problems raised in the literature concerning the Lagrangian and the Hamiltonian formulations: We prove their equivalence, make clear the role of the homogeneity preserving diffeomorphisms in the phase space approach, and show that the number of physical degrees of freedom is the same in the Hamiltonian and Lagrangian formulations. Residual gauge transformations play an important role in our approach, and we suggest that Poincaré transformations for special relativistic systems can be understood as residual gauge transformations. In the Appendixes, we give the general computation of the equations of motion and the Lagrangian for any Bianchi-type vacuum metric and for spatially homogeneous Maxwell fields in a nondynamical background (with zero currents). We also illustrate our counting of degrees of freedom in an appendix.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time.