Hysteresis in a system driven by either generalized force or displacement variables: Martensitic phase transition in single-crystalline<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Cu</mml:mi><mml:mtext>−</mml:mtext><mml:mi>Zn</mml:mi><mml:mtext>−</mml:mtext><mml:mi>Al</mml:mi></mml:mrow></mml:math>

Bonnot, Erell; Romero, Ricardo; Illa, Xavier; Mañosa, Lluı́s; Planes, Antoni; Vives, Eduard

doi:10.1103/physrevb.76.064105

Cited by 29 publications

(28 citation statements)

References 27 publications

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“…Although the precise behavior of the complexity in the vicinity of the "knees" is still unknown (and is certainly different on the Bethe and on euclidian lattices), it is now clear that the discontinuity in the hysteresis loop associated with a macroscopic avalanche is due to the existence of a gap in the magnetization of the metastable states for a range of applied field. Consequently, by controlling the magnetization instead of the magnetic field [9], one should observe a reentrant loop, as indeed observed in some magnetic materials [1] and other disordered systems [21,22]. Finally, one may wonder whether the most numerous, hence probable, states in the middle of the loop are accessible dynamically; it is, however, dubious that this can be achieved by performing a deep quench from T = ∞ to T = 0 at a fixed field [23].…”

Section: Resultsmentioning

confidence: 99%

TheT= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

2009

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Abstract.In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T = 0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean-field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is positive everywhere inside). On the other hand, the occurence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied field, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.The T = 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metast

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Section: Resultsmentioning

confidence: 99%

TheT= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

2009

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“…For stress-driven experiments we used a machine which enables control of the force applied to the sample while elongation was continuously monitored [6]. The machine applies a dead load to the sample which can be increased or decreased at a well controlled rate.…”

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Elastocaloric Effect Associated with the Martensitic Transition in Shape-Memory Alloys

et al. 2008

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The elastocaloric effect in the vicinity of the martensitic transition of a Cu-Zn-Al single crystal has been studied by inducing the transition by strain or stress measurements. While transition trajectories show significant differences, the entropy change associated with the whole transformation (S t ) is coincident in both kinds of experiments since entropy production is small compared to S t . The values agree with estimations based on the Clausius-Clapeyron equation. The possibility of using these materials for mechanical refrigeration is also discussed. DOI: 10.1103/PhysRevLett.100.125901 PACS numbers: 65.40.Gÿ, 75.30.Sg, 81.30.Kf Caloric effects are expected to occur under the application of an external field to a given material. The elastocaloric effect [1] is the mechanical analogue of the magnetocaloric effect that has received considerable attention in the recent years owing to its potential use for environmentally friendly refrigeration [2]. The magnetocaloric effect is related to the isothermal change of entropy or the adiabatic change of temperature that takes place within a material when a magnetic field is applied or removed. This effect originates from the coupling between the magnetic sublattice and an externally applied magnetic field and thus occurs in any magnetic material. A large effect is expected in the vicinity of field-induced, firstorder phase transitions where large entropy changes should occur [3]. By analogy, the elastocaloric effect is defined as the isothermal change of entropy or the adiabatic change of temperature that takes place when a mechanical field (stress) is applied or released in a given material. Indeed, this effect is expected to be a consequence of the coupling between an external applied stress and the lattice. Continuing with the analogy, a large elastocaloric effect is also foreseen in systems undergoing stress-induced, first-order phase transitions. Good candidates to show this effect are shape-memory alloys. These materials undergo a diffusionless purely structural transition from a cubic to a lower symmetry phase that can be stress induced [4]. Actually, shape-memory properties are related to this transition and refer to the ability of these systems to remember their original shape after severe deformation [5].In contrast to magnetism, instead of controlling the applied stress (or force) which is the variable thermodynamically equivalent to the magnetic field, in mechanical experiments, the system is usually driven by controlling the strain (generalized displacement) which is the conjugated variable to the stress in the way that magnetization is the conjugated variable of the magnetic field. In magnetic systems, due to the difficulty in controlling magnetization, magnetization-driven experiments aimed at studying the magnetocaloric effect have not, to our knowledge, been reported. Thus, comparing results from both field-or stress-driven and magnetization or strain-driven experiments is of general interest since constraining the (generalized) displacement pr...

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“…9,10 The driving mechanism has been argued to strongly influence the transition path. [11][12][13][14][15] The two important extreme driving situations consist of controlling either the externally applied field or its corresponding generalized displacement ͑thermodynamically conjugated variable͒. In the first case, driving is soft in the sense that displacement is free to fluctuate, while it is hard in the second case since displacement is constrained by the driving device.…”

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Driving-induced crossover in the avalanche criticality of martensitic transitions

et al. 2009

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An experimental study of the statistical distribution of acoustic emission avalanches in martensitic transitions is presented. The critical exponents characterizing the power-law distributions of avalanches are measured as a function of cycling under soft-driving ͑stress-driving͒ and hard-driving ͑strain-driving͒ procedures. Results provide experimental support for a recent theory based on a spin model that predicts a crossover from classical criticality in the soft-driving case to self-organized criticality in the hard-driving case.

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Hysteresis in a system driven by either generalized force or displacement variables: Martensitic phase transition in single-crystallineCu−Zn−Al

Cited by 29 publications

References 27 publications

TheT= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

TheT= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

Elastocaloric Effect Associated with the Martensitic Transition in Shape-Memory Alloys

Driving-induced crossover in the avalanche criticality of martensitic transitions

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