# Acoustic Emission Spectroscopy: Applications in Geomaterials and Related Materials
## 2 Avalanches and Acoustic Emission Spectroscopy  
When physical systems produce discontinuous burst responses under external fields, the bursts often follow the predictions of avalanche physics and 'crackling noise' emitters [6, 9, 10]. Typical examples include natural avalanche disasters, such as earthquakes [11, 12]. The avalanche behavior does not depend on the size of the earthquake with pico-scale earthquakes and global earthquakes following very similar patterns. Avalanche dynamics also describe the fluctuations of stock markets, which have small fluctuations and stock disasters caused by financial crisis [6], the temporary evolution of neuron connectors during 'thinking' processes [13, 14, 15], and the medical deterioration of brain structures [16, 17]. Other examples are the Barkhausen 'noise' of pinned domain walls during magnetization processes [18, 19, 20, 21], martensitic transformations [22, 23], plastic deformation in solids [24], materials failure [25], ferroelectric and ferroelastic domain movements [3, 26, 27, 28, 29] etc. Avalanche events are monitored by different monitoring methods, such as force drop measurement [30], optical observation [28], thermal radiation observation [23], etc. Acoustic emission (AE) spectroscopy has become the method of choice in many fields [5, 31, 32, 33] because it is highly sensitive. For example, the AE system constructed by the Vallen company, Germany, has a sampling rate that can reach up to 10 MHz, an arrival time resolution of 100 ns, and an energy resolution of 1.8 \(\times\) 10\({}^{-18}\) V\({}^{2}\)s (i.e., in the attojoule regime, aJ) referred to sensor signal at 34 dB preamplifier gain. A previous study showed simultaneous measurements of the avalanche of stress and AE during mechanically induced twin boundary motion in a shape memory alloy. It showed that the probability of finding an AE event during a stress drop is \(\sim\)100 times higher than between stress drops. Additionally, the relations between mechanical energy drops and the lower bound of the acoustic emitted energy is approximately proportional [34]. The common drawback of AE is that the local signal is first locally transferred into an acoustic signal inside the sample which then propagates as an acoustic wavelet to the noise detector. The wave profile of AE is hence determined only indirectly by the initial signal and great care has to be taken not to confuse the measured signal with that of the initial atomic event. This problem has been analyzed in great detail [35], the analytical techniques highlight the strong similarity with the deconvolution procedure to analyze propagating waves in the context of geophysical seismology. The current statistical analysis of AE signals, especially its energy probability distribution function (PDF) and the interevent times, are not much affected by wave profiles and there is a large amount of literature which elucidates some of the intricacies of AE spectroscopy [36, 37, 38, 35]. The AE signal is in the form of a wave in Figure 1, and the important parameters of AE waves are their amplitude, duration, rise time, absolute energy, and waiting time. The amplitude A(t) is a function of time t and captures the evolution of the conjugate parameter to the external force. The time evolution of the amplitude is typically initiated by an incubation period where A(t) increases exponentially leading to the maximum amplitude, called A\({}_{\text{max}}\). The duration is the time period over which an avalanche survives. Experimental time scales typically extend from a few microseconds to many milliseconds. Absolute energies are obtained by numerical integration of the square voltage of signals E = 1/R \(\int_{\text{ti}}^{\text{j}}\text{U}^{2}(\text{t})\text{dt}\), where t\({}_{\text{i}}\) and t\({}_{\text{j}}\) are starting and ending times of the signal and R = 10 k\(\Omega\) is a reference resistance. The rise time is the time difference between starting time of a wavelet and time of the wave peak.