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

Temporal average shapes of crackling noise avalanches, (Formula presented.) ((Formula presented.) 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, (Formula presented.), energy, (Formula presented.), size (area), (Formula presented.) and duration, (Formula presented.)), which in the mean field theory (MFT) have the form (Formula presented.), (Formula presented.), (Formula presented.). Recently, it turned out that normalizing the theoretically predicted average (Formula presented.) function at a fixed size, (Formula presented.) ((Formula presented.) and (Formula presented.) are non-universal, material-dependent constants) by (Formula presented.) and the rising time, (Formula presented.), a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation (Formula presented.) too, where (Formula presented.) is a mechanism-dependent constant. It was shown that (Formula presented.) also appears in the scaling relations (Formula presented.) and (Formula presented.), 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 (Formula presented.) 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 Ni₅₀Mn_28.5Ga_21.5 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 (Formula presented.), and the voltage axis with (Formula presented.), 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 (Formula presented.) 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.