Experiments and Models of Avalanches in Martensites

Abstract

We have studied the kinetics of thermoelastic martensitic transformations (MT), both experimentally and using spin models. Measurements of acoustic emission and thermal pulses in Cu-Zn-A1 single crystals, during thermally and stress induced MT, show that the transformation takes place as a sequence of avalanches, whose sizes and durations distribute according to power laws in more than one decade. Most features observed are qualitatively reproduced by spin models that incorporate domain interactions and frozen disorder. A systematic simulation of these models at T = 0 (no fluctuations allowed) has shown that there is a critical concentration of disorder for which avalanche sizes and durations distribute following power-laws, which appear to be independent of details of the models other than their dimensionality. We discuss the connection between the experimental results and the simulations.

Thermally activated avalanches: Jamming and the progression of needle domains

“…Our results for the power law distribution at modest temperatures just below T VF show power law behavior with exponent α ≈ 2 which is identical to those one would expect for avalanche statistics with large defect concentrations 64 .…”

Pathways of structural and magnetic transition in ferromagnetic shape-memory alloys

“…[23][24][25][26][27][28][29][30][31] In particular, Vives et al 32 have studied acoustic emissions in a nonmagnetic Cu-Zn-Al shape-memory alloy. They have observed avalanchelike behavior associated with the formation of nonmagnetic martensite plates.…”

Crackling noise

“…42,43 ) Researchers have studied many systems that crackle. Simple models have been developed to study bubbles rearranging in foams as they are sheared, 44 biological extinctions 45 (where the models are controversial: 46,47 of course we personally believe that the asteroid did in the dinosaurs), fluids invading porous materials and other problems involving invading fronts [48][49][50][51][52][53] (where the model we describe was invented 48,49 ), the dynamics of superconductors 54-54.4 and superfluids, 55,56 sound emitted during martensitic phase transitions, 57 fluctuations in the stock market, 58,59 solar flares, 60 cascading failures in power grids, 61,62 failures in systems designed for optimal performance, [63][64][65] group decision making, 65.1 and fracture in disordered materials. 65.2-65.7 These models are driven systems with many degrees of freedom, which respond to the driving in a series of discrete avalanches spanning a broad range of scales -what we are calling crackling noise.…”