Calorimetric and acoustic emission study of martensitic transformation in single-crystalline ${\mathrm{Ni}}_2\mathrm{MnGa}$ alloys

The jerky character of austenite-martensite phase transformation in ${\mathrm{Ni}}_2\mathrm{MnGa}$ single crystals (with 10M martensite structure) has been investigated by thermal cycling using a differential scanning calorimeter (DSC) and by detection of acoustic emissions (AEs) at low cooling and heating rates (0.1 K/min and below). It is illustrated that, besides the low cooling and heating rate, mass and surface roughness are also important parameters in optimizing the best signal/noise ratio in order to obtain individual peaks suitable for statistical analysis. Three types of samples, differing in the twin structure and twin boundary behavior, were investigated with and without surface roughening made by electro-erosion. The statistical analysis, carried out for both (thermal and acoustic) types of signals, provided power-law behavior. In calorimetric measurements the energy exponents, obtained in cooling, were the same within the experimental errors $\left(\varepsilon =1.7\pm 0.2\right)$ for the three samples investigated. In acoustic emission experiments the energy and amplitude, $\alpha$, exponents were determined both for cooling and heating. The exponents for cooling and heating runs are slightly different. They are larger for heating for both $\alpha$ and $\varepsilon$, in accordance with the asymmetric acoustic activity: we observed higher acoustic activity (higher number of hits) during cooling. The effect of the surface roughness is negligible in the exponents (but higher acoustic activity corresponds to higher roughness) and the following values were obtained: $\varepsilon =1.5\pm 0.1$ and $\alpha =2.1\pm 0.1$ for cooling as well as $\varepsilon =1.8\pm 0.1$ and $\alpha =2.6\pm 0.1$ for heating. Our results are in accordance with the results of Gallardo et al. [Phys. Rev. B 81, 174102 (2010)] obtained in Cu based alloys: the exponents of the energy distributions, for both DSC and AE signals, were the same within the experimental errors. Furthermore, our exponents obtained from the AE measurements are close to the values obtained by Ludwig et al. ($\alpha =2.6\pm 0.1$ and $\varepsilon =1.75\pm 0.1$) [App. Phys. Lett. 94 121901 (2009)] and Niemann et al. ($\varepsilon =1.9\pm 0.1$) [Phys. Rev. B 86, 214101 (2012)] in ${\mathrm{Ni}}_2\mathrm{MnGa}$ alloys with similar 10M martensite structure.

Figure 1

Effect of cooling rate on the shape of DSC curves for the shot-peened sample ($m=59$ mg).

Figure 2

DSC results for cooling: heat flow (mW) versus temperature on the surface-roughened not-treated sample (cooling rate 0.02K/min, $m=36$ mg).

Figure 3

DSC curve during heating on the same sample shown in Fig. 2 (heating rate: 0.02 K/min).

Figure 4

$logP$ versus $logE$ for cooling (summarized over 40 cycles) for the surface-roughened not-treated sample.

Figure 5

Typical acoustic signal and measured parameters.

Figure 6

Acoustic activity during heating and cooling (0.1 K/min) in the shot-peened sample. Points indicate the amplitudes of hits (since, as indicated in Table 2, a very large number of hits were observed, for the sake of clarity only every 15th of them are presented). The upper continuous curve gives the sum or integral of amplitudes. Main jumps on this curve (T1 and T2) coincide well with the time window where the DSC activity was observed.

Figure 7

$logP$ versus $logE$, constructed from acoustic emission hits during cooling, for the surface-roughened shot-peened sample. Each point is calculated from large amount of hits (see also TABLE II). Note that the bins on the horizontal axis are logarithmic bins and the vertical axis is normalized by the linear bin width.

Figure 8

$logP$ versus $logA$, constructed from acoustic emission hits during cooling, for the surface-roughened shot-peened sample (see also the caption fod Fig. 7.).

Figure 9

Power-law exponent, $\alpha$, as a function of $A_{\min }$, using the maximum likelihood method. The horizontal line indicates the value obtained from a linear fitting of the $logP$ versus $logA$ function.

Figure 10

Dependence of energy exponents of the not-treated sample on the number of heating cycles.