Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni2MnGa

Abstract

Temporal average shapes of crackling noise avalanches, U(t) (U is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, A, energy, E, size (area), S, and duration, T), which in the mean field theory (MFT) have the form E∝A3, S∝A2, S∝T2. Recently, it turned out that normalizing the theoretically predicted average U(t) function at a fixed size, U(t)=atexp−bt2 (a and b are non-universal, material-dependent constants) by A and the rising time, R, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation R~A1−φ too, where φ is a mechanism-dependent constant. It was shown that φ also appears in the scaling relations E~A3−φ and S~A2−φ, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with φ= 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni50Mn28.5Ga21.5 single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with A1−φ, and the voltage axis with A, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the φ values are in accordance with theoretical predictions going beyond the MFT, but the AE results for φ are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.

Acoustic emissions from spin crossover complexes

“…Furthermore, it was found that, t B R and a B A j in eqn (3), and thus scaling the voltage by A and the time by A (1Àj) , nice common functions were obtained for the motion of interfaces between austenite and martensite phases in ferromagnetic shape memory single crystals, 51 and for the motion of an individual twin boundary in a Ni 2 MnGa single crystal as well. 59 It was also shown that the value of j also appears in the scaling exponents x = 2 À j as well as y = 3 À j. 51 Since the experimental determination of j from the rising time versus amplitude relation is difficult (R is usually very short), we estimated j from the average values of x and y.…”