Avalanche criticalities and elastic and calorimetric anomalies of the transition from cubic Cu-Al-Ni to a mixture of $18R$ and $2H$ structures

We studied the two-step martensitic transition of a Cu-Al-Ni shape-memory alloy by calorimetry, acoustic emission (AE), and resonant ultrasound spectroscopy (RUS) measurements. The transition occurs under cooling from the cubic $(\beta , Fm3m)$ parent phase near 242 K to a mixture of orthorhombic $2H$ and monoclinic $18R$ phases. Heating leads first to the back transformation of small $18R$ domains to $\beta$ and/or $2H$ near 255 K, and then to the transformation $2H$ to $\beta$ near 280 K. The total transformation enthalpy is $\mathrm{\Delta }{H}_T=328\pm 10$ J/mol and is observed as one large latent heat peak under cooling. The back-transformation entropy under heating breaks down into a large component $18R$ to $\beta$ at 255 K and a smaller, smeared component of the transformation $2H$ to $\beta$ near 280 K. The proportions inside the phase mixture depend on the thermal history of the sample. The elastic response of the sample is dominated by large elastic softening during cooling. The weakening of the elastic shear modulus shows a peak at 242 K, which is typical for the formation of complex microstructures. Cooling the sample further leads to additional changes of the microstructure and domain wall freezing, which is seen by gradual elastic hardening and increasing damping of the RUS signal. Heating from 220 K to room temperature leads to elastic anomalies due to the initial transformation, which is now shifted to high temperatures. The transition is smeared over a wider temperature interval and shows strong elastic damping. The shear modulus of the cubic phase is recovered at 280 K. The phase transformation leads to avalanches, which were recorded by AE and by time-resolved calorimetry. The cooling transition shows very extended avalanche signals in calorimetry with power-law distributions. Cooling and heating runs show AE signals over a large temperature interval above 260 K. Splitting the transformation into two martensite phases leads to power-law exponents $\varepsilon \sim 2$ $(\beta \leftrightarrow 18R)$ and $\varepsilon \sim 1.5$ $(\beta \leftrightarrow 2H)$ while the phase mixture shows an effective AE exponent of 1.7.

Figure 1

Grain size distribution of the studied sample. The continuous line is a log-normal fit.

Figure 2

DTA traces for heating (red) and cooling (blue) experiments. Data corresponding to cooling experiments have been changed in sign to allow a better comparison to heating data.

Figure 3

Integrated transition enthalpy for heating (red) and cooling (blue) runs. The total enthalpy change is identical within experimental errors. The right scale gives the corresponding transformed fraction.

Figure 4

Activity plots of avalanches obtained from calorimetric measurements during (a) heating and (b) cooling runs. Activity is measured by counting the number of spikes larger than 23 $\mu \mathrm{J}$ in intervals of half a Kelvin. Smooth continuous lines display a fit of the sum of two Gaussian distributions.

Figure 5

Log-log plot of the distribution of energies (linear bins) of the spikes detected from calorimetric measurements. Data recorded during the heating run are split at $T=260$ K separating the contributions to the activity observed in Fig. 4. Straight lines display best power-law fits to experimental data.

Figure 6

Heat flux versus temperature for several runs: step1, cooling from room temperature to 220 K (blue line); step 2, heating from 220 K to 260 K (red line); step 3, cooling from 260 K to 220 K (black line); step 4, heating from 220 K to room temperature (magenta line).

Figure 7

Enthalpy excess (obtained from integration of calorimetric curves) versus temperature for several runs: step 1, cooling from room temperature to 220 K (blue line); step 2, heating from 220 K to 260 K (read line); step 3, cooling from 260 K to 220 K (black line); heating from 220 K to room temperature (magenta line). The dotted red line represents the enthalpy for the initial heating run.

Figure 8

(a) AE energy cumulated in bins of 2 s as a function of temperature during cooling from 320 K down to 220 K (blue) and subsequent heating up to 320 K (red). (b) AE activity recorded during the same runs (using also bins of 2 s). The arrows indicate the range for the analysis presented in Fig. 9.

Figure 9

(a) Log-log plot of the distribution of avalanche energies (in aJ) for complete cooling and heating runs. (b) Distribution of avalanche energies (in aJ) for signals detected in the temperature interval 230–250 K (corresponding to the $18R \to \beta$ transition) and 270–290 K (corresponding to the $2H \to \beta$ transition) respectively. The intervals are indicated in Fig. 8.

Figure 10

Likelihood plots corresponding to the distributions shown in Figs. 8 and 8.

Figure 11

RUS frequencies (a) and damping (b) during cooling and heating experiments. The sample was first cooled to 220 K, then heated to 260 K, recooled to 220 K and finally heated to room temperature. The minima in the squared RUS frequency and the maximum of the damping $Q^{-1}$ are close to the transformation instability points, which show with thermal history. The gradual changes below 242 K show that the $18R$+$2H$ phase mixture is not athermal at low temperatures.